A349589 E.g.f. satisfies: A(x) * log(A(x)) = 1 - exp(-x*A(x)).

1, 1, 0, -4, -3, 87, 230, -4583, -27216, 434928, 4871719, -62913079, -1240374960, 12230778601, 426135019232, -2759957884648, -189393687667107, 479371576805751, 105233549909615798, 233116575802412969, -71022416772836562008, -574100485456271792020

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..425

Formula

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

Mathematica

a[n_] := Sum[(-1)^(n - k)*(n - k + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, Nov 23 2021 *)

Prog

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

Crossrefs

Cf. A141209, A349587, A349588.

Cf. A349558.

Sequence in context: A371687 A299188 A300026 * A362736 A266255 A351792

Adjacent sequences: A349586 A349587 A349588 * A349590 A349591 A349592

Keyword

sign

Author

Seiichi Manyama, Nov 22 2021

Status

approved