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A373861
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a(n) = Sum_{k=0..n} k^(2*n) * |Stirling1(n,k)|.
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1
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1, 1, 17, 923, 107724, 22369324, 7385651720, 3597082257152, 2449105468081600, 2238708422118782376, 2661994302285967390224, 4014423110086784061347592, 7519716937006429200213786240, 17194081369411703462470895338272
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: Sum_{k>=0} (-log(1 - k^2*x))^k / k!.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k^(2*n)*abs(stirling(n, k, 1)));
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CROSSREFS
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KEYWORD
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nonn,new
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AUTHOR
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STATUS
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approved
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