OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..390
FORMULA
a(n) = Sum_{k=0..n} 3^k * k! * Stirling1(n,k).
a(n) ~ n! * exp(1/3) / (3*(exp(1/3)-1)^(n+1)). - Vaclav Kotesovec, Jun 12 2020
a(0) = 1; a(n) = 3 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, May 22 2022
MATHEMATICA
a[n_] := Sum[k! * 3^k * StirlingS1[n, k], {k, 0, n}]; Array[a, 21, 0] (* Amiram Eldar, Jun 12 2020 *)
With[{nn=20}, CoefficientList[Series[1/(1-3Log[1+x]), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Oct 02 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, 3^k*k!*stirling(n, k, 1));
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-3*log(1+x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v; \\ Seiichi Manyama, May 22 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 12 2020
STATUS
approved