A104872 Diagonal sums of A004248.
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
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..681
Programs
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PARI
a(n) = sum(k=0, n\2, k^(n-2*k)); \\ Seiichi Manyama, Apr 09 2022
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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
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