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 1-4 of 4 results.

A377451 E.g.f. satisfies A(x) = 1/(1 - A(x)^4 * (exp(x) - 1)).

Original entry on oeis.org

1, 1, 11, 241, 8171, 377401, 22118531, 1572752161, 131565858491, 12661132904521, 1378019469008051, 167374385250354481, 22443998566390975211, 3293411316452536046041, 524941525063836265071971, 90316250360918785641307201, 16682672480771981403086626331, 3292860351837963891732540729961
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (5*k)!/(4*k+1)!*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (5*k)!/(4*k+1)! * Stirling2(n,k).

A377453 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x) - 1))^3.

Original entry on oeis.org

1, 3, 33, 639, 18177, 687663, 32585793, 1858893039, 124128928257, 9502575055983, 820716875385153, 78959656742857839, 8375163183606235137, 971063889443489669103, 122194096152956362997313, 16586054767142612489229039, 2415658529914018225123490817, 375779208568915395913102663023
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377450.
a(n) = 3 * Sum_{k=0..n} (4*k+2)!/(3*k+3)! * 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).

A377489 E.g.f. satisfies A(x) = 1/(1 - A(x)^2 * (exp(x) - 1))^2.

Original entry on oeis.org

1, 2, 24, 548, 18996, 889532, 52623924, 3767367788, 316781141316, 30608709436412, 3342279339791124, 407043376061484428, 54704971792071412836, 8042679084840031176092, 1284038419974274852278324, 221234151594672691543079468, 40916180234895561309469607556
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2*sum(k=0, n, (5*k+1)!/(4*k+2)!*stirling(n, k, 2));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377451.
a(n) = 2 * Sum_{k=0..n} (5*k+1)!/(4*k+2)! * Stirling2(n,k).
Showing 1-4 of 4 results.