login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A349883
Expansion of Sum_{k>=0} (k * x)^k/(1 - k^3 * x).
4
1, 1, 5, 60, 1242, 41241, 2033683, 141318208, 13262986788, 1624337451945, 252725477615989, 48858277079478156, 11523986801592238046, 3265676705193282018577, 1097336766468309067029991, 432291795385094609190468384, 197690320046319097006619353352
OFFSET
0,3
LINKS
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
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 *)
PROG
(PARI) a(n, t=3) = sum(k=0, n, k^(t*(n-k)+k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^3*x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 03 2021
STATUS
approved