A354416 Expansion of e.g.f. (1 - log(1-x))^x.

1, 0, 2, 0, 16, 5, 288, 392, 9840, 33462, 582910, 3652044, 55557192, 524095728, 7910319116, 98390834310, 1573086910848, 23774700449584, 414180226506456, 7249907657342184, 138771378745878680, 2735366111451910944, 57469663931297252976, 1253755421949789141624

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} k * A089064(k-1) * binomial(n-1,k-1) * a(n-k).

a(n) ~ (n-1)!. - Vaclav Kotesovec, Jun 08 2022

Prog

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

Crossrefs

Cf. A089064, A351739, A354083.

Sequence in context: A155585 A350972 A236755 * A057375 A009045 A060313

Adjacent sequences: A354413 A354414 A354415 * A354417 A354418 A354419

Keyword

nonn

Author

Seiichi Manyama, May 26 2022

Status

approved