A349557 E.g.f. satisfies: log(A(x)) = (exp(x*A(x)) - 1) * A(x).

1, 1, 6, 68, 1163, 26787, 778128, 27325321, 1126308870, 53323302708, 2851990661789, 170088808988705, 11192134680722586, 805521092432042573, 62950026461699015998, 5308512876799649771192, 480492707646769163920059, 46464318322169305448661915

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..345

Formula

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

a(n) ~ sqrt(s^3 * (1+s) / (1 + r^2*s^2*(1+s) + r*s*(3 + 2*s))) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.1609673785833512641321517974482987852086944930869... and s = 1.597727491873940099115048788232158935283220293884... are real roots of the system of equations exp(r*s)*s = s + log(s), exp(r*s)*(1 + r*s) = 1 + 1/s. - Vaclav Kotesovec, Nov 22 2021

Mathematica

a[n_] := Sum[(n + k + 1)^(k - 1) * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Nov 22 2021 *)

Prog

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

Crossrefs

Cf. A052880, A349558, A349560.

Sequence in context: A256238 A359714 A370938 * A140606 A355219 A014505

Adjacent sequences: A349554 A349555 A349556 * A349558 A349559 A349560

Keyword

nonn

Author

Seiichi Manyama, Nov 21 2021

Status

approved