The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A354287 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A354287

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

#15 by Vaclav Kotesovec at Mon May 23 09:24:22 EDT 2022

STATUS

editing

approved

#14 by Vaclav Kotesovec at Mon May 23 09:24:18 EDT 2022

FORMULA

a(n) ~ exp((-5 + 1/(exp(1/3) - 1) + 4*sqrt(3*n/(exp(1/3) - 1)) - 4*n)/6) * n^(n - 1/4) / (sqrt(2) * 3^(1/4) * (exp(1/3) - 1)^(n + 1/4)). - Vaclav Kotesovec, May 23 2022

STATUS

approved

editing

#13 by Michael De Vlieger at Mon May 23 09:11:22 EDT 2022

STATUS

proposed

approved

#12 by Seiichi Manyama at Mon May 23 08:21:21 EDT 2022

STATUS

editing

proposed

#11 by Seiichi Manyama at Mon May 23 07:44:51 EDT 2022

DATA

1, 3, 30, 438, 8334, 194580, 5368662, 170591022, 6126386724, 245127214548, 10804866210648, 519910458588576, 27105081897342816, 1521393008601586536, 91445577404393807928, 5858664681621903625368, 398467273528657973600208, 28668189882264862351707504

#10 by Seiichi Manyama at Mon May 23 03:43:55 EDT 2022

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} A354263(k) * binomial(n-1,k-1) * a(n-k).

#9 by Seiichi Manyama at Mon May 23 03:28:01 EDT 2022

PROG

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 3^k*k!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;

#8 by Seiichi Manyama at Mon May 23 03:06:11 EDT 2022

CROSSREFS

Cf. A000262, A354263, A354289, A354291.

#7 by Seiichi Manyama at Mon May 23 02:15:47 EDT 2022

FORMULA

a(n) = Sum_{k=0..n} 3^k * A000262(k) * |Stirling1(n, k)|.

#6 by Seiichi Manyama at Mon May 23 02:08:09 EDT 2022

FORMULA

a(n) = Sum_{k=0..n} 3^k * A000262(k) * |Stirling1(n, k)|.