login
A353993
Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^(1/(1-x)).
4
1, 1, 8, 63, 668, 7850, 115914, 1847286, 34031024, 682177464, 15049816200, 357564279600, 9212847784392, 252552128708568, 7395084613746816, 229412209982127480, 7524339637608261120, 259675490280634374720, 9418707076419411194304, 357606237255136232451264
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A353992(k) * binomial(n-1,k-1) * a(n-k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-k*x^k)^(1/(1-x))))
(PARI) a353992(n) = n!*sum(k=1, n, sumdiv(k, d, (k/d)^d/d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a353992(j)*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 06 2022
STATUS
approved