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A249459
a(n) = Sum_{k=0..n} k^(2*n).
13
1, 1, 17, 794, 72354, 10874275, 2438235715, 762963987380, 317685943157892, 169842891165484965, 113394131858832552133, 92465351109879998121806, 90431265068257318469676710, 104479466717230437574945525959, 140782828210237288756752539959687
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Sum_{n>=0} exp(n^2*x).
a(n) ~ exp(2)/(exp(2)-1) * n^(2*n).
G.f.: Sum_{k>=0} (k^2 * x)^k/(1 - k^2 * x). - Seiichi Manyama, Dec 03 2021
MATHEMATICA
Table[Sum[k^(2*n), {k, 1, n}], {n, 1, 20}]
Table[n!*SeriesCoefficient[Sum[Exp[k^2*x], {k, 1, n}], {x, 0, n}], {n, 1, 20}]
PROG
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp(k*x+x*O(x^n))^k), n);
for(n=1, 20, print1(a(n), ", "))
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1-k^2*x))) \\ Seiichi Manyama, Dec 03 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 29 2014
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, Dec 03 2021
STATUS
approved