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A123114
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a(n) = Sum_{r>0,s>0} binomial(r*s-1,n-1)/2^(r+s).
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1
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1, 3, 13, 83, 701, 7363, 92541, 1354627, 22636861, 425241347, 8871085565, 203487078403, 5090418231549, 137920771272963, 4023549748488445, 125743894742698243, 4191213031967650813, 148414827031140706307
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (1/(n-1)!)*Sum_{k=1..n} Stirling1(n,k)*b(k)^2, where b(n) = Sum_{k=1..n} (k-1)!*Stirling2(n,k).
a(n) ~ c * (n-1)! / (log(2))^(2*n), where c = 2^(-log(2)/2) = 0.7864497045594053649114085152934509198700275589579678941719548714254307448... - Vaclav Kotesovec, Jun 07 2019
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MATHEMATICA
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Table[Sum[StirlingS1[n, k]*(Sum[(j - 1)!*StirlingS2[k, j], {j, 1, k}])^2, {k, 1, n}]/(n-1)!, {n, 1, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)
Table[-(-1)^n + Sum[StirlingS1[n, k]*PolyLog[1-k, 2]^2, {k, 2, n}]/(n-1)!, {n, 1, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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