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A373861

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

1, 1, 17, 923, 107724, 22369324, 7385651720, 3597082257152, 2449105468081600, 2238708422118782376, 2661994302285967390224, 4014423110086784061347592, 7519716937006429200213786240, 17194081369411703462470895338272

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

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

MATHEMATICA

Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; nmax=13; Range[0, nmax]!CoefficientList[Series[Sum[(-Log[1 - k^2*x])^k / k!, {k, 0, nmax}], {x, 0, nmax}], x] (* Stefano Spezia, Jun 19 2024 *)

PROG

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

CROSSREFS

Cf. A229261, A351183, A373856.

Sequence in context: A086265 A156138 A229261 * A196873 A262386 A298302

Adjacent sequences: A373858 A373859 A373860 * A373862 A373863 A373864

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 19 2024

STATUS

approved

URL: https://oeis.org/A373861

⇱ A373861 - OEIS