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.

A062810 a(n) = Sum_{i=1..n} i^(n - i) + (n - i)^i.

Original entry on oeis.org

1, 3, 7, 17, 45, 131, 419, 1465, 5561, 22755, 99727, 465537, 2303829, 12037571, 66174411, 381560425, 2301307841, 14483421859, 94909491607, 646309392369, 4565559980989, 33401808977411, 252713264780595, 1974606909857945
Offset: 1

Views

Author

Olivier Gérard, Jun 23 2001

Keywords

Crossrefs

Programs

  • Mathematica
    Sum[i^(n - i) + (n - i)^i, {i, 1, n}]
  • PARI
    a(n) = sum(i=1, n, i^(n-i) + (n-i)^i); \\ Michel Marcus, Mar 24 2019

Formula

a(n) = 2 * A026898(n-1) - 1.
a(n) = 2 * A003101(n-1) + 1.

A062812 a(n) = Sum_{i=1..n} i^(n - i) + (-1)^(n - i)*(n - i)^i.

Original entry on oeis.org

1, 1, 5, 9, 25, 65, 205, 713, 2753, 11425, 50389, 234825, 1155817, 6009153, 32958173, 190115849, 1148816017, 7244099617, 47521750501, 323632894729, 2284774880441, 16702573959489, 126299702576365, 986688266888777
Offset: 1

Views

Author

Olivier Gérard, Jun 23 2001

Keywords

Crossrefs

Programs

  • Mathematica
    Sum[i^(n - i) + (-1)^(n - i)*(n - i)^i, {i, 1, n}]
  • PARI
    a(n) = sum(i=1, n, i^(n-i) + (-1)^(n-i)*(n-i)^i); \\ Michel Marcus, Mar 24 2019

A353016 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).

Original entry on oeis.org

1, 1, 1, 2, 5, 11, 33, 108, 357, 1405, 5713, 24670, 117413, 574007, 3004577, 16608120, 95057925, 576245913, 3622049809, 23693870554, 161816447365, 1140392550275, 8351286979745, 63206781102116, 493344133444389, 3980464191557205, 33029872125113937, 282290255465835382
Offset: 0

Views

Author

Seiichi Manyama, Apr 16 2022

Keywords

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := Sum[(n-2*k)^(2*k), {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 16 2022 *)
  • PARI
    a(n) = sum(k=0, n\2, (n-2*k)^(2*k));
    
  • PARI
    my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^2)))

Formula

G.f.: Sum_{k>=0} x^k / (1 - (k * x)^2).
a(n) = (A062811(n) + 1)/2 for n > 0. - Hugo Pfoertner, Apr 16 2022
Showing 1-3 of 3 results.