A359659 a(n) = Sum_{k=0..n} k^(k * (n-k+1)).
1, 2, 6, 45, 1051, 88602, 27121964, 37004504305, 198705527223757, 5595513387083114570, 686714367475480207331582, 468422339816915120237104999421, 1664212116512828935888786624225704855
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..51
Programs
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PARI
a(n) = sum(k=0, n, k^(k*(n-k+1)));
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^k*x))) -
PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k+1)^(k+1)*x)))
Formula
G.f.: Sum_{k>=0} (k * x)^k/(1 - k^k * x).
G.f.: Sum_{k>=0} x^k/(1 - (k+1)^(k+1) * x).
a(n) = A349893(n+1) - 1.