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A192565
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a(n) = sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*k!^2,k=0..n).
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0
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1, 1, 7, 119, 3766, 191074, 14190940, 1451180016, 195500153984, 33556323694176, 7148802130010784, 1850863101948856368, 572367322411341168960, 208372437783910651168800, 88211625475147231105812096, 42967145403522500557662391104
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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) ~ c * LambertW(-1, -r*exp(-r))^n * n!^2 / (sqrt(n) * LambertW(-exp(-1/r)/r)^n), where r = 0.673313285145753168... is the root of the equation (1 + 1/(r*LambertW(-exp(-1/r)/r))) * (r + LambertW(-1, -r*exp(-r))) = 1 and c = 0.5694875599509546909505843910919946016728003129830561427442509356... - Vaclav Kotesovec, Jul 05 2021
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MATHEMATICA
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Table[Sum[Abs[StirlingS1[n+1, k+1]]StirlingS2[n, k]k!^2, {k, 0, n}], {n, 0, 100}]
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PROG
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(Maxima) makelist(sum(abs(stirling1(n+1, k+1))*stirling2(n, k)*k!^2, k, 0, n), n, 0, 24);
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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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