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A104872
Diagonal sums of A004248.
8
1, 0, 1, 1, 2, 3, 6, 12, 27, 64, 163, 441, 1268, 3855, 12344, 41464, 145653, 533736, 2036149, 8071785, 33192790, 141351715, 622384730, 2829417276, 13263528351, 64038928728, 318121600695, 1624347614737, 8517247764136, 45822087138879
OFFSET
0,5
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} k^(n-2*k).
G.f.: Sum_{k>=0} x^(2*k) / (1 - k * x). - Seiichi Manyama, Apr 09 2022
a(n) ~ sqrt(Pi) * (n/(2*LambertW(exp(1)*n/2)))^(n + 1/2 - n/LambertW(exp(1)*n/2)) / sqrt(1 + LambertW(exp(1)*n/2)). - Vaclav Kotesovec, Apr 14 2022
PROG
(PARI) a(n) = sum(k=0, n\2, k^(n-2*k)); \\ Seiichi Manyama, Apr 09 2022
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k*x))) \\ Seiichi Manyama, Apr 09 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 28 2005
STATUS
approved