cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A349889 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n).

Original entry on oeis.org

1, 1, 15, 666, 59230, 8775075, 1948891581, 605698755508, 250914820143996, 133610836793706405, 88919025666286620475, 72317513878698256697166, 70571883548815735717843290, 81383769918571603591381635271
Offset: 0

Views

Author

Seiichi Manyama, Dec 04 2021

Keywords

Crossrefs

Programs

  • Mathematica
    Join[{1},Table[Sum[(-1)^(n-k) k^(2n),{k,0,n}],{n,20}]] (* Harvey P. Dale, Nov 19 2023 *)
  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*k^(2*n));
    
  • PARI
    my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1+k^2*x)))

Formula

G.f.: Sum_{k>=0} (k^2 * x)^k/(1 + k^2 * x).
a(n) ~ 1/(1 + exp(-2)) * n^(2*n). - Vaclav Kotesovec, Dec 10 2021

A349894 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*(n-k)).

Original entry on oeis.org

1, 0, 1, -3, -10, 410, 42985, -6527829, -24060996846, -6613442955828, 3882375189467092921, 235121650953066124724477, -289337164954511885810252000250, -995208334663809003504695464745010282, 13325880481925983143500510271865447222057073
Offset: 0

Views

Author

Seiichi Manyama, Dec 04 2021

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*k^(k*(n-k)));
    
  • PARI
    my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^k*x)))

Formula

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

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

Views

Author

Seiichi Manyama, Dec 05 2021

Keywords

Crossrefs

Programs

  • Mathematica
    Join[{1},Table[Sum[(-1)^(n-k) k^(3n),{k,0,n}],{n,20}]] (* Harvey P. Dale, Apr 12 2022 *)
  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*k^(3*n));
    
  • PARI
    my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1+k^3*x)))

Formula

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
Showing 1-3 of 3 results.