A349883 Expansion of Sum_{k>=0} (k * x)^k/(1 - k^3 * x).
1, 1, 5, 60, 1242, 41241, 2033683, 141318208, 13262986788, 1624337451945, 252725477615989, 48858277079478156, 11523986801592238046, 3265676705193282018577, 1097336766468309067029991, 432291795385094609190468384, 197690320046319097006619353352
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..227
Programs
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Mathematica
a[n_] := Sum[If[k == 3*n - 2*k == 0, 1, k^(3*n - 2*k)], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Dec 04 2021 *) -
PARI
a(n, t=3) = sum(k=0, n, k^(t*(n-k)+k));
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^3*x)))
Formula
a(n) = Sum_{k=0..n} k^(3*n-2*k).
a(n) ~ sqrt(Pi) * (3/2)^(1/2 + 3*n - 3*n/LambertW(3*exp(1)*n/2)) * (n/LambertW(3*exp(1)*n/2))^(1/2 + 3*n - 3*n/LambertW(3*exp(1)*n/2)) / sqrt(1 + LambertW(3*exp(1)*n/2)). - Vaclav Kotesovec, Dec 04 2021