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A351133
a(n) = Sum_{k=0..n} k! * k^(2*n) * Stirling1(n,k).
6
1, 1, 31, 3992, 1342294, 932514674, 1161340476698, 2356863300156504, 7278091701243797640, 32477694155566998880608, 201155980661221409458717152, 1674230688936725338278370413264, 18235249164492209082483584810706528
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Sum_{k>=0} log(1 + k^2*x)^k.
a(n) ~ c * d^n * n^(3*n + 1/2), where d = 0.3417329834649268103028466896966197580428514873775849996969994420891... and c = 2.92355271092039591960355156784704285135358... - Vaclav Kotesovec, Feb 03 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[k! * k^(2*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 02 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*k^(2*n)*stirling(n, k, 1));
(PARI) first(n)=my(x='x+O('x^(n+1))); Vec(serlaplace(sum(k=0, n, log(1+k^2*x)^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 02 2022
STATUS
approved