The On-Line Encyclopedia of Integer Sequences (OEIS)

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A049120

Row sums of triangle A049029.
(history; published version)

#15 by Harvey P. Dale at Tue Sep 10 09:21:21 EDT 2019

STATUS

editing

approved

#14 by Harvey P. Dale at Tue Sep 10 09:21:18 EDT 2019

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[-1+1/Surd[1-4x, 4]]-1, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 10 2019 *)

STATUS

approved

editing

#13 by Russ Cox at Sat Mar 31 13:19:59 EDT 2012

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

Wolfdieter Lang

Discussion

Sat Mar 31

13:19

OEIS Server: https://oeis.org/edit/global/878

#12 by Russ Cox at Fri Mar 30 18:49:54 EDT 2012

FORMULA

Representation of a(n) as the n-th moment of a positive function on positive half-axis (Stieltjes moment problem), in Maple notation: a(n)=int(x^n*exp(-1)*exp(-1/4*x)*(1/96*x*hypergeom([],[5/4, 3/2, 7/4, 2],1/1024*x)+ 1/8*4^(3/4)*x^(1/4)/Pi*2^(1/2)*GAMMA(3/4)*hypergeom([],[1/4, 1/2,3/4, 5/4],1/1024*x)+1/8*4^(1/2)*x^(1/2)/Pi^(1/2)*hypergeom([],[1/2, 3/4, 5/4,3/2],1/1024*x)+1/24*4^(1/4)*x^(3/4)/GAMMA(3/4)*hypergeom([],[3/4, 5/4, 3/2,7/4],1/1024*x))/x, x=0..infinity),n=1,2... . - _Karol A. Penson (penson(AT)lptl.jussieu.fr), _, Dec 16 2007

Discussion

Fri Mar 30

18:49

OEIS Server: https://oeis.org/edit/global/243

#11 by T. D. Noe at Fri Nov 25 22:54:47 EST 2011

STATUS

editing

approved

#10 by T. D. Noe at Fri Nov 25 22:54:43 EST 2011

FORMULA

a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator (1+x)^5*d/dx. Cf. A000110, A000262, A049118 and A049119 . - Peter Bala, Nov 25 2011

STATUS

proposed

editing

#9 by Peter Bala at Fri Nov 25 06:35:25 EST 2011

STATUS

editing

proposed

#8 by Peter Bala at Fri Nov 25 06:35:04 EST 2011

FORMULA

a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator (1+x)^5*d/dx. Cf. A000110, A000262, A049118 and A049119 - Peter Bala, Nov 25 2011

CROSSREFS

Cf. A049119, generalized Bell numbers B(4, 1, n). A049118.

STATUS

approved

editing

#7 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

CROSSREFS

Cf. A049119, generalized Bell numbers B(4, 1, n).

KEYWORD

easy,nonn,new

#6 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

FORMULA

Representation of a(n) as the n-th moment of a positive function on positive half-axis (Stieltjes moment problem), in Maple notation: a(n)=int(x^n*exp(-1)*exp(-1/4*x)*(1/96*x*hypergeom([],[5/4, 3/2, 7/4, 2],1/1024*x)+ 1/8*4^(3/4)*x^(1/4)/Pi*2^(1/2)*GAMMA(3/4)*hypergeom([],[1/4, 1/2,3/4, 5/4],1/1024*x)+1/8*4^(1/2)*x^(1/2)/Pi^(1/2)*hypergeom([],[1/2, 3/4, 5/4,3/2],1/1024*x)+1/24*4^(1/4)*x^(3/4)/GAMMA(3/4)*hypergeom([],[3/4, 5/4, 3/2,7/4],1/1024*x))/x, x=0..infinity),n=1,2... . - Karol A. Penson (penson(AT)lptl.jussieu.fr), Dec 16 2007

KEYWORD

easy,nonn,new