A346984 Expansion of e.g.f. 1 / (6 - 5 * exp(x))^(1/5).

1, 1, 7, 85, 1495, 34477, 983983, 33476437, 1322441575, 59492222077, 3002578396255, 168005805229285, 10321907081030167, 690761732852321677, 50015387402165694607, 3895721046926471861365, 324805103526730206129607, 28861947117644330678207389, 2722944810091827410698112959

Offset

0,3

Comments

Stirling transform of A008548.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..351

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k) * A008548(k).

a(n) ~ n! / (Gamma(1/5) * 6^(1/5) * n^(4/5) * log(6/5)^(n + 1/5)). - Vaclav Kotesovec, Aug 14 2021

O.g.f. (conjectural): 1/(1 - x/(1 - 6*x/(1 - 6*x/(1 - 12*x/(1 - 11*x/(1 - 18*x/(1 - ... - (5*n-4)*x/(1 - 6*n*x/(1 - ... ))))))))) - a continued fraction of Stieltjes-type. - Peter Bala, Aug 22 2023

a(0) = 1; a(n) = Sum_{k=1..n} (5 - 4*k/n) * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 09 2023

a(0) = 1; a(n) = a(n-1) - 6*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Nov 16 2023

Maple

g:= proc(n) option remember; `if`(n<2, 1, (5*n-4)*g(n-1)) end:
b:= proc(n, m) option remember;
     `if`(n=0, g(m), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..18);  # Alois P. Heinz, Aug 09 2021

Mathematica

nmax = 18; CoefficientList[Series[1/(6 - 5 Exp[x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]

Crossrefs

Cf. A000670, A008548, A094418, A305404, A346982, A346983, A346985, A352117, A352118, A352119.

Sequence in context: A302565 A369372 A049412 * A361065 A056547 A293055

Adjacent sequences: A346981 A346982 A346983 * A346985 A346986 A346987

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Aug 09 2021

Status

approved