The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111578 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A111578

Triangle T(n, m) = T(n-1, m-1) + (4m-3)*T(n-1, m) read by rows 1<=m<=n.
(history; published version)

#19 by Alois P. Heinz at Fri Sep 06 22:23:06 EDT 2024

STATUS

proposed

approved

#18 by Jason Yuen at Fri Sep 06 22:04:20 EDT 2024

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editing

proposed

#17 by Jason Yuen at Fri Sep 06 22:04:06 EDT 2024

FORMULA

O.g.f. column k: 1/( (1 - x)*(1 - 5*x)*...*(1 - (4*k + 1)*x ) ). (End)

EXAMPLE

1;

1,1;

1,6,1;

1,31,15,1;

1,156,166,28,1;

STATUS

approved

editing

#16 by N. J. A. Sloane at Sun May 16 21:59:53 EDT 2021

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proposed

approved

#15 by F. Chapoton at Sun May 16 15:02:51 EDT 2021

STATUS

editing

proposed

#14 by F. Chapoton at Sun May 16 15:02:45 EDT 2021

PROG

(Python)

def A096038(n, m):

if n < 1 or m < 1 or m > n:

return 0

elif n <=2:

return 1

else:

(Python) def A096038(n, m): ...if n < 1 or m < 1 or m > n: ......return 0 ...elif n <=2: ......return 1 ...else: ...... return A096038(n-1, m-1)+(4*m-3)*A096038(n-1, m)

print( [A096038(n, m) for n in range(20) for m in range(1, n+1)] ) # _R. J. Mathar_, Oct 11 2009

# R. J. Mathar, Oct 11 2009

STATUS

approved

editing

Discussion

Sun May 16

15:02

F. Chapoton: indent py code

#13 by N. J. A. Sloane at Wed Feb 04 23:34:48 EST 2015

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proposed

approved

#12 by Jean-François Alcover at Wed Jan 28 07:34:17 EST 2015

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editing

proposed

#11 by Jean-François Alcover at Wed Jan 28 07:34:07 EST 2015

MATHEMATICA

T[n_, k_] := 1/(4^(k-1)*(k-1)!) * Sum[ (-1)^(k-j-1) * (4*j+1)^(n-1) * Binomial[k-1, j], {j, 0, k-1}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jan 28 2015, after Peter Bala *)

STATUS

proposed

editing

#10 by Peter Bala at Tue Jan 27 07:07:30 EST 2015

STATUS

editing

proposed