The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A367139 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A367139

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

#13 by Vaclav Kotesovec at Tue Nov 07 11:32:28 EST 2023

STATUS

editing

approved

#12 by Vaclav Kotesovec at Tue Nov 07 11:32:16 EST 2023

FORMULA

a(n) ~ LambertW(3*exp(4))^n * n^(n-1) / (sqrt(3*(1 + LambertW(3*exp(4)))) * exp(n) * (-3 + LambertW(3*exp(4)))^(4*n + 1)). - Vaclav Kotesovec, Nov 07 2023

#11 by Vaclav Kotesovec at Tue Nov 07 11:29:40 EST 2023

MATHEMATICA

Table[1/(3*n+1)! * Sum[(3*n+k)! * Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)

STATUS

approved

editing

#10 by Michael De Vlieger at Mon Nov 06 07:14:50 EST 2023

STATUS

proposed

approved

#9 by Seiichi Manyama at Mon Nov 06 06:47:14 EST 2023

STATUS

editing

proposed

#8 by Seiichi Manyama at Mon Nov 06 06:42:53 EST 2023

FORMULA

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

#7 by Seiichi Manyama at Mon Nov 06 06:21:31 EST 2023

FORMULA

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

#6 by Seiichi Manyama at Mon Nov 06 06:13:49 EST 2023

CROSSREFS

Cf. A367135, A367137.

#5 by Seiichi Manyama at Mon Nov 06 05:53:22 EST 2023

DATA

1, 1, 9, 167, 4780, 186004, 9173780, 548563140, 38573633016, 3119384230176, 285237426927552, 29102185296785160, 3277703460197645232, 403931173342682581296, 54066960915411480743520, 7811249803193620134996864, 1211525560869437165319590400

#4 by Seiichi Manyama at Mon Nov 06 05:52:50 EST 2023

PROG

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