A349602 E.g.f. satisfies: A(x) * log(A(x)) = 1 - exp(-x*A(x)^2).

1, 1, 2, 2, -43, -668, -5908, -1209, 1399400, 37121106, 508366819, -3012861630, -444910083132, -15407930598279, -249403814792546, 5359691081465462, 589889204153846141, 23861630070579997032, 379819221897309026072, -21971010821241361939769

Offset: 0

Author

Seiichi Manyama, Nov 22 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..390

Crossrefs

Cf. A216135, A349600, A349601.

Cf. A349585, A349589.

Programs

Mathematica

a[n_] := Sum[(-1)^(n - k)*(2*n - k + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Nov 23 2021 *)

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*(2*n-k+1)^(k-1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (2*n-k+1)^(k-1) * Stirling2(n,k).