The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A355398

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

A355398

Expansion of e.g.f. exp(exp(3*x)/3 - exp(2*x)/2 + 1/6).
(history; published version)

#13 by Vaclav Kotesovec at Tue Jul 05 02:24:19 EDT 2022

STATUS

editing

approved

#12 by Vaclav Kotesovec at Tue Jul 05 02:22:23 EDT 2022

FORMULA

a(n) ~ exp(exp(3*r)/3 - exp(2*r)/2 + 1/6 - n) * (n/r)^(n + 1/2) / sqrt((1 + 3*r)*exp(3*r) - (1 + 2*r)*exp(2*r)), where r = LambertW(3*n)/3 - 1/(2 + 3/LambertW(3*n) - 3^(4/3) * n^(1/3) * (1 + LambertW(3*n)) / LambertW(3*n)^(4/3)). - Vaclav Kotesovec, Jul 05 2022

STATUS

approved

editing

#11 by Michael De Vlieger at Thu Jun 30 14:44:27 EDT 2022

STATUS

proposed

approved

#10 by Vaclav Kotesovec at Thu Jun 30 13:46:44 EDT 2022

STATUS

editing

proposed

#9 by Vaclav Kotesovec at Thu Jun 30 13:46:30 EDT 2022

MATHEMATICA

nmax = 20; CoefficientList[Series[Exp[Exp[3*x]/3 - Exp[2*x]/2 + 1/6], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 30 2022 *)

STATUS

proposed

editing

#8 by Seiichi Manyama at Thu Jun 30 11:39:54 EDT 2022

STATUS

editing

proposed

#7 by Seiichi Manyama at Thu Jun 30 11:39:25 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, (3^(j-1)-2^(j-1))*binomial(i-1, j-1)*v[i-j+1])); v;

#6 by Seiichi Manyama at Thu Jun 30 11:35:31 EDT 2022

DATA

1, 0, 1, 5, 22, 115, 761, 5880, 49897, 460045, 4621366, 50385555, 590795217, 7389964400, 98105330961, 1377426850805, 20388005470582, 317112889169555, 5167636268318921, 88001180739368680, 1562559584723343417, 28871671817796197885, 554116841783123679446

#5 by Seiichi Manyama at Thu Jun 30 11:03:38 EDT 2022

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(3*x)/3-exp(2*x)/2+1/6)))

#4 by Seiichi Manyama at Thu Jun 30 11:03:00 EDT 2022

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} (3^(k-1) - 2^(k-1)) * binomial(n-1,k-1) * a(n-k).