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 1-5 of 5 results.

A371271 E.g.f. satisfies A(x) = 1 + x*A(x)^3 * (exp(x*A(x)^2) - 1).

Original entry on oeis.org

1, 0, 2, 3, 124, 725, 28146, 352807, 14395256, 298559529, 13269150190, 394087597211, 19361289265044, 752705527798237, 41083484117561354, 1970818974867113295, 119467697774656366576, 6792102349650727753553, 455778318504089893121766
Offset: 0

Views

Author

Seiichi Manyama, Mar 16 2024

Keywords

Crossrefs

Programs

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

Formula

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

A371270 E.g.f. satisfies A(x) = 1 + x*A(x)^2 * (exp(x*A(x)^2) - 1).

Original entry on oeis.org

1, 0, 2, 3, 100, 605, 18366, 238147, 7688584, 162016857, 5839673410, 172051422191, 7034104918380, 265080848463301, 12311587474831750, 561485310426413115, 29475848282815342096, 1569372890780660724401, 92402629467727290784650
Offset: 0

Views

Author

Seiichi Manyama, Mar 16 2024

Keywords

Crossrefs

Programs

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

Formula

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

A371269 E.g.f. satisfies A(x) = 1 + x*A(x) * (exp(x*A(x)^2) - 1).

Original entry on oeis.org

1, 0, 2, 3, 76, 485, 10746, 146167, 3552312, 75642345, 2150551990, 61400333291, 2061654862356, 72804918721405, 2858153637295698, 119363732105632575, 5395737275060765296, 259270058379207421649, 13294348104095211012462, 721446934706871966578899
Offset: 0

Views

Author

Seiichi Manyama, Mar 16 2024

Keywords

Crossrefs

Programs

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

Formula

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

A377690 E.g.f. satisfies A(x) = 1 + x * (exp(x*A(x)^3) - 1).

Original entry on oeis.org

1, 0, 2, 3, 76, 545, 11166, 175777, 4012856, 96530625, 2685888730, 83721921041, 2843440273092, 107065956887617, 4332658616388662, 190612061432096865, 8961290146870598896, 451334805268791262337, 24156272027391899229234, 1371678815491898403876913
Offset: 0

Views

Author

Seiichi Manyama, Nov 04 2024

Keywords

Crossrefs

Programs

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

Formula

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

A377688 E.g.f. satisfies A(x) = (1 + x * (exp(x*A(x)) - 1))^2.

Original entry on oeis.org

1, 0, 4, 6, 128, 850, 13872, 195314, 3586592, 74163618, 1694735840, 44196946882, 1244904944208, 38788984768274, 1302631536943856, 47297768099973330, 1840951270666885952, 76501162074673415746, 3382517582789739956928, 158445187728836733069986
Offset: 0

Views

Author

Seiichi Manyama, Nov 04 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371262.
a(n) = 2 * n! * Sum_{k=0..floor(n/2)} (2*n-2*k+1)! * Stirling2(n-k,k)/( (n-k)! * (2*n-3*k+2)! ).
Showing 1-5 of 5 results.