A373858 a(n) = Sum_{k=1..n} k! * k^(2*n-1) * Stirling1(n,k).
0, 1, 15, 1268, 317294, 175542694, 181641609214, 315309390376056, 850661260866748728, 3370191684116333977872, 18768704088141613880906736, 141902519646656406912522712848, 1415862822521619228707500717132224, 18210234893009450819658863637633454608
Offset: 0
Keywords
Programs
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Mathematica
nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(Log[1 + k^2*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *) -
PARI
a(n) = sum(k=1, n, k!*k^(2*n-1)*stirling(n, k, 1));
Formula
E.g.f.: Sum_{k>=1} log(1 + k^2*x)^k / k.