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.

A377454 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x) - 1))^4.

Original entry on oeis.org

1, 4, 56, 1384, 50216, 2422024, 146279816, 10633540264, 904699882856, 88234503004744, 9707888368200776, 1189726637663987944, 160741241332049376296, 23738834426406792534664, 3804763374380021378204936, 657774175587674349626736424, 122016250347540672925706274536
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 4*sum(k=0, n, (5*k+3)!/(4*k+4)!*stirling(n, k, 2));

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377451.
a(n) = 4 * Sum_{k=0..n} (5*k+3)!/(4*k+4)! * Stirling2(n,k).

A377450 E.g.f. satisfies A(x) = 1/(1 - A(x)^3 * (exp(x) - 1)).

Original entry on oeis.org

1, 1, 9, 157, 4209, 153301, 7075209, 395858317, 26043658209, 1970447255941, 168569253106809, 16090431675455677, 1695423031884496209, 195469637688003331381, 24477403062879209570409, 3308367753565825806208237, 480047805083610542972470209, 74429414765710201956179803621
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (4*k)!/(3*k+1)!*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (4*k)!/(3*k+1)! * Stirling2(n,k).

A377452 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x) - 1))^2.

Original entry on oeis.org

1, 2, 16, 224, 4612, 126392, 4340836, 179534504, 8693925172, 482731239032, 30243460133956, 2110849596096584, 162438922745208532, 13665129603889106072, 1247684652874279407076, 122885960933254703151464, 12987106624622962667192692, 1466014441678589235669027512
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2*sum(k=0, n, (3*k+1)!/(2*k+2)!*stirling(n, k, 2));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367161.
a(n) = 2 * Sum_{k=0..n} (3*k+1)!/(2*k+2)! * Stirling2(n,k).
Showing 1-3 of 3 results.