A354083 Expansion of e.g.f. (1 + log(1-x))^x.

1, 0, -2, -6, -16, -55, -288, -2128, -19808, -219546, -2816530, -41002236, -666782136, -11961352104, -234327748900, -4972665181170, -113552835539328, -2774993356571920, -72238332282154344, -1995222148760626392, -58268719729725843880, -1793842001139571701696

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} A052809(k) * binomial(n-1,k-1) * a(n-k).

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, j*sum(k=1, j-1, (k-1)!*abs(stirling(j-1, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A052809, A351739, A354416.

Sequence in context: A147927 A147919 A320805 * A150029 A221841 A068787

Adjacent sequences: A354080 A354081 A354082 * A354084 A354085 A354086

Keyword

sign

Author

Seiichi Manyama, May 26 2022

Status

approved