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A308490
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a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(2*k).
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7
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1, 1, 17, 778, 70023, 10439451, 2327592658, 725325847443, 301054612941037, 160546901676583432, 106969402879501806589, 87079496403914056543799, 85043317211453886535179728, 98135961356804028347727824541, 132097548629285541942722646521053
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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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a(n) ~ exp(exp(-2)/2) * n^(2*n).
E.g.f.: Sum_{k>=0} (k^2 * (exp(x) - 1))^k / k!. - Seiichi Manyama, Feb 04 2022
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MATHEMATICA
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Join[{1}, Table[Sum[k^(2*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 20}]]
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*(exp(x)-1))^k/k!))) \\ Seiichi Manyama, Feb 04 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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