The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A367158 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A367158

E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x).
(history; published version)

#10 by Vaclav Kotesovec at Fri Nov 10 04:29:56 EST 2023

STATUS

editing

approved

#9 by Vaclav Kotesovec at Fri Nov 10 04:29:51 EST 2023

FORMULA

a(n) ~ 9 * n^(n-1) / (2^(5/2) * exp(23*n/27) * (exp(4/27) - 1)^(n - 1/2)). - Vaclav Kotesovec, Nov 10 2023

#8 by Vaclav Kotesovec at Fri Nov 10 04:23:48 EST 2023

MATHEMATICA

Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS1[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 10 2023 *)

STATUS

approved

editing

#7 by Michael De Vlieger at Tue Nov 07 08:24:08 EST 2023

STATUS

proposed

approved

#6 by Seiichi Manyama at Tue Nov 07 06:41:00 EST 2023

STATUS

editing

proposed

#5 by Seiichi Manyama at Tue Nov 07 05:49:22 EST 2023

CROSSREFS

Cf. A367155, A367161, A367164.

#4 by Seiichi Manyama at Tue Nov 07 02:39:11 EST 2023

FORMULA

a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * |Stirling1(n,k)|.

#3 by Seiichi Manyama at Tue Nov 07 02:38:47 EST 2023

CROSSREFS

Cf. A052803.

#2 by Seiichi Manyama at Tue Nov 07 02:38:26 EST 2023

NAME

allocated for Seiichi Manyama

E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x).

DATA

1, 1, 7, 92, 1824, 48804, 1649724, 67492872, 3243567552, 179139978072, 11181615816216, 778466939121552, 59811143359463952, 5027200928936108064, 458865351655379262432, 45201262487568977507328, 4779609140451030860102400, 539990133396500652971120640

OFFSET

0,3

PROG

(PARI) a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*abs(stirling(n, k, 1)));

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Nov 07 2023

STATUS

approved

editing

#1 by Seiichi Manyama at Tue Nov 07 02:38:26 EST 2023

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved