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.

A357662 Expansion of e.g.f. cosh( (exp(3*x) - 1)/sqrt(3) ).

Original entry on oeis.org

1, 0, 3, 27, 198, 1485, 12825, 132678, 1582497, 20603727, 284290560, 4132840239, 63571690485, 1038868740000, 18022911716439, 330305863479615, 6355242571945878, 127721845479277737, 2672729031195365949, 58142565625982730462, 1313557910179640120061
Offset: 0

Views

Author

Seiichi Manyama, Oct 07 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cosh((exp(3*x)-1)/sqrt(3)))))
    
  • PARI
    a(n) = sum(k=0, n\2, 3^(n-k)*stirling(n, 2*k, 2));

Formula

a(n) = Sum_{k=0..floor(n/2)} 3^(n-k) * Stirling2(n,2*k).

A357664 Expansion of e.g.f. sinh( (exp(2*x) - 1)/sqrt(2) )/sqrt(2).

Original entry on oeis.org

0, 1, 2, 6, 32, 220, 1592, 11944, 96000, 847120, 8209952, 86020704, 958326272, 11243157952, 138464594816, 1789358629504, 24250275913728, 344002396594432, 5092763802452480, 78443316497892864, 1253887341918199808, 20761127890765634560
Offset: 0

Views

Author

Seiichi Manyama, Oct 07 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(2*x)-1)/sqrt(2))/sqrt(2)))))
    
  • PARI
    a(n) = sum(k=0, (n-1)\2, 2^(n-1-k)*stirling(n, 2*k+1, 2));

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 2^(n-1-k) * Stirling2(n,2*k+1).

A357666 Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.

Original entry on oeis.org

0, 1, 4, 20, 160, 1872, 25024, 348224, 5055488, 78571776, 1332573184, 24695206912, 493816963072, 10492449771520, 234399640633344, 5480635606908928, 134015043318054912, 3427700843478056960, 91642829715498336256, 2556218693498006929408
Offset: 0

Views

Author

Seiichi Manyama, Oct 07 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/2)/2)))
    
  • PARI
    a(n) = sum(k=0, (n-1)\2, 4^(n-1-k)*stirling(n, 2*k+1, 2));

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 4^(n-1-k) * Stirling2(n,2*k+1).
Showing 1-3 of 3 results.