The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A370937 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A370937

Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - log(1+3*x)/3) ).
(history; published version)

#9 by Michael De Vlieger at Wed Mar 06 08:00:00 EST 2024

STATUS

proposed

approved

#8 by Seiichi Manyama at Wed Mar 06 06:26:51 EST 2024

STATUS

editing

proposed

#7 by Seiichi Manyama at Wed Mar 06 05:48:16 EST 2024

CROSSREFS

Cf. A198860, A370936.

#6 by Seiichi Manyama at Wed Mar 06 05:46:45 EST 2024

FORMULA

a(n) = (1/(n+1)!) * Sum_{k=0..n} 3^(n-k) * (n+k)! * Stirling1(n,k).

#5 by Seiichi Manyama at Wed Mar 06 05:42:10 EST 2024

LINKS

<a href="/index/Res#revert">Index entries for reversions of series</a>

#4 by Seiichi Manyama at Wed Mar 06 05:18:57 EST 2024

DATA

1, 1, 1, 3, 12, 54, 432, 2862, 29880, 311688, 3530952, 52947432, 694960560, 12339656640, 208855024128, 3885592056624, 84031138091520, 1688108258868480, 41851910546369280, 986544325475565696, 25610732492679696384, 720669291974958124800, 19681263432530494848000

#3 by Seiichi Manyama at Wed Mar 06 05:17:49 EST 2024

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-log(1+3*x)/3))/x))

(PARI) a(n) = sum(k=0, n, 3^(n-k)*(n+k)!*stirling(n, k, 1))/(n+1)!;

#2 by Seiichi Manyama at Wed Mar 06 05:16:18 EST 2024

NAME

allocated for Seiichi Manyama

Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - log(1+3*x)/3) ).

DATA

1, 1, 1, 3, 12, 54, 432, 2862, 29880, 311688, 3530952, 52947432, 694960560, 12339656640, 208855024128, 3885592056624, 84031138091520, 1688108258868480, 41851910546369280

OFFSET

0,4

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Mar 06 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Wed Mar 06 05:16:18 EST 2024

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved