A349885 -id:A349885 - cp's OEIS frontend

A349884 Expansion of Sum_{k>=0} (k * x)^k/(1 + k^2 * x).

1, 1, 3, 12, 76, 961, 15407, 221528, 3260936, 80774113, 2462081967, 50963779604, 922244742292, 61063845514113, 2868669700179871, 2019727494212912, -47889136910252848, 461395118866593115713, 5781219348638565771423, -2108738296748190078596084

Offset: 0

Seiichi Manyama, Dec 03 2021

sign

Cf. A120485, A349885.

Cf. A349856, A349859, A349863.

a[n_] := Sum[If[k == 2*n - k == 0, 1, (-1)^(n - k) * k^(2*n - k)], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Dec 04 2021 *)

a(n, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^k);

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1+k^2*x)))

a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n-k).

A349902 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n).

Original entry on oeis.org

1, 1, 63, 19172, 16249870, 29458152441, 97813591721181, 537081363012854224, 4535464309375188976956, 55796581668379082029481225, 958824462567528346234944706075, 22255431432328421226838750870120356, 678866987929798923743810982299237129610

Offset: 0

Seiichi Manyama, Dec 05 2021

nonn

Cf. A120485, A349885, A349889, A349891.

Join[{1},Table[Sum[(-1)^(n-k) k^(3n),{k,0,n}],{n,20}]] (* Harvey P. Dale, Apr 12 2022 *)

a(n) = sum(k=0, n, (-1)^(n-k)*k^(3*n));

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1+k^3*x)))

G.f.: Sum_{k>=0} (k^3 * x)^k/(1 + k^3 * x).

a(n) ~ 1/(1 + exp(-3)) * n^(3*n). - Vaclav Kotesovec, Dec 10 2021

cp's OEIS Frontend

A349884 Expansion of Sum_{k>=0} (k * x)^k/(1 + k^2 * x).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A349902 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula