A351133 a(n) = Sum_{k=0..n} k! * k^(2*n) * Stirling1(n,k).

1, 1, 31, 3992, 1342294, 932514674, 1161340476698, 2356863300156504, 7278091701243797640, 32477694155566998880608, 201155980661221409458717152, 1674230688936725338278370413264, 18235249164492209082483584810706528

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..162

Formula

E.g.f.: Sum_{k>=0} log(1 + k^2*x)^k.

a(n) ~ c * d^n * n^(3*n + 1/2), where d = 0.3417329834649268103028466896966197580428514873775849996969994420891... and c = 2.92355271092039591960355156784704285135358... - Vaclav Kotesovec, Feb 03 2022

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^(2*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 02 2022 *)

Prog

(PARI) a(n) = sum(k=0, n, k!*k^(2*n)*stirling(n, k, 1));
(PARI) first(n)=my(x='x+O('x^(n+1))); Vec(serlaplace(sum(k=0, n, log(1+k^2*x)^k)))

Crossrefs

Cf. A006252, A320083, A351134.

Cf. A229260, A351135, A351136.

Sequence in context: A289397 A177465 A187755 * A350721 A115736 A110848

Adjacent sequences: A351130 A351131 A351132 * A351134 A351135 A351136

Keyword

nonn

Author

Seiichi Manyama, Feb 02 2022

Status

approved