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 1-2 of 2 results.

A259323 2*A259322(n).

Original entry on oeis.org

2, 1460, 32710, 268008, 1330890, 4874012, 14527630, 37308880, 85584018, 179675780, 351208022, 647279800, 1135561050, 1910402028, 3100048670, 4875056032, 7457991970, 11134523220, 16265976038, 23303463560, 32803672042, 45446398140, 62053929390, 83612360048, 111294934450, 146487510052
Offset: 1

Views

Author

N. J. A. Sloane, Jun 24 2015

Keywords

Crossrefs

Cf. A259322.

Programs

  • PARI
    Vec(2*x*(x^6+722*x^5+10543*x^4+23548*x^3+10543*x^2+722*x+1)/(x-1)^8 + O(x^100)) \\ Colin Barker, Jun 29 2015
    
  • PARI
    a(n) = n*(384*n^6-672*n^4+392*n^2-62)/21 \\ Charles R Greathouse IV, Jun 29 2015

Formula

a(n) = 2*(n*(-31+196*n^2-336*n^4+192*n^6))/21. - Colin Barker, Jun 29 2015
G.f.: 2*x*(x^6+722*x^5+10543*x^4+23548*x^3+10543*x^2+722*x+1) / (x-1)^8. - Colin Barker, Jun 29 2015

A349490 Sum of the n-th powers of the first n odd numbers.

Original entry on oeis.org

1, 10, 153, 3108, 79225, 2437006, 87922513, 3642188936, 170423429841, 8891285549650, 511800291063721, 32222868466588460, 2202868653419747209, 162509566498902542934, 12868118600594014094625, 1088626666242258867384848, 97994054039441765759931169
Offset: 1

Views

Author

Seiichi Manyama, Dec 09 2021

Keywords

Crossrefs

Sum of the k-th powers of the first n odd numbers: A000290 (k=1), A000447 (k=2), A002593 (k=3), A002309 (k=4), A002594 (k=5), A259322 (k=6).

Programs

  • Mathematica
    Table[Sum[(2*k-1)^n, {k,1,n}], {n,1,20}] (* Vaclav Kotesovec, Dec 09 2021 *)
  • PARI
    a(n) = sum(k=1, n, (2*k-1)^n);

Formula

a(n) = Sum_{k=1..n} (2*k-1)^n.
a(n) ~ 2^n * n^n / (exp(1/2) - exp(-1/2)). - Vaclav Kotesovec, Dec 09 2021
Showing 1-2 of 2 results.