A349587 E.g.f. satisfies: A(x)^A(x) = 1 + x*A(x).

1, 1, 0, -3, 4, 60, -294, -2800, 34504, 197568, -6087360, -9146808, 1488986808, -5886157992, -469973309064, 5492298353880, 177826238321856, -4277426240130048, -72353540601814464, 3537861051231290880, 22847222673714931200, -3226666120379253611136

Offset: 0

Author

Seiichi Manyama, Nov 22 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..421

Crossrefs

Cf. A141209, A349588, A349589.

Cf. A120980, A162655, A162656.

Programs

Mathematica

a[n_] := Sum[(n - k + 1)^(k - 1)*StirlingS1[n, k], {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, Nov 23 2021 *)

PARI

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

Formula

a(n) = Sum_{k=0..n} (n-k+1)^(k-1) * Stirling1(n,k).