A354316 Expansion of e.g.f. 1/(1 + x/3 * log(1 - 3 * x)).

1, 0, 2, 9, 96, 1170, 18324, 340200, 7360128, 181476288, 5024611440, 154319988240, 5206240427904, 191372822989920, 7612497915813504, 325791049256094240, 14925809593280332800, 728828735500650355200, 37786217117138333005824

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-2*k) * k! * |Stirling1(n-k,k)|/(n-k)!.

Mathematica

With[{nn=20}, CoefficientList[Series[1/(1+x/3 Log[1-3x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 06 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/3*log(1-3*x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 3^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\2, 3^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A052830, A354315.

Cf. A354310.

Sequence in context: A011837 A106343 A086992 * A345466 A115965 A001142

Adjacent sequences: A354313 A354314 A354315 * A354317 A354318 A354319

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved