OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..162
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