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.

A377323 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3)/A(x).

Original entry on oeis.org

1, 1, 5, 53, 884, 20234, 589834, 20903700, 872660256, 41944510752, 2281437791448, 138539360885760, 9290720296262976, 681965664411820944, 54384461861952738528, 4682101594725064872768, 432815761314471190599936, 42757813607285233998385920, 4495579313771176952867958528
Offset: 0

Views

Author

Seiichi Manyama, Oct 24 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..n} (3*n-k)!/(3*n-2*k+1)! * |Stirling1(n,k)|.

A377349 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2)/A(x)^2.

Original entry on oeis.org

1, 1, 1, 8, 62, 744, 11102, 201704, 4323720, 106591584, 2974873656, 92674125840, 3188299718496, 120053825169888, 4911082489042992, 216879763758962688, 10283600782413709056, 521088305671611058176, 28101278301136842204288, 1606968565080853531472640
Offset: 0

Views

Author

Seiichi Manyama, Oct 26 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..floor((2*n+1)/3)} (2*n-2*k)!/(2*n-3*k+1)! * |Stirling1(n,k)|.

A377350 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3)/A(x)^3.

Original entry on oeis.org

1, 1, 1, 11, 108, 1584, 29808, 674988, 18091944, 557844408, 19468760904, 758698622472, 32653135227936, 1538316755200224, 78737559447563136, 4350956519444451840, 258163046132873143680, 16370486288763937324416, 1104824513292622360789248, 79068747951669626322531840
Offset: 0

Views

Author

Seiichi Manyama, Oct 26 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..floor((3*n+1)/4)} (3*n-3*k)!/(3*n-4*k+1)! * |Stirling1(n,k)|.

A377358 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x))/A(x) )^2.

Original entry on oeis.org

1, 2, 4, 22, 194, 2268, 34272, 624804, 13432120, 332078160, 9286572624, 289821031344, 9985648515504, 376489542984384, 15418392593403360, 681562973789926560, 32345053760113660800, 1640243700728870131200, 88516191520113318169344, 5064936155664187593030912
Offset: 0

Views

Author

Seiichi Manyama, Oct 26 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377349.
a(n) = 2 * Sum_{k=0..floor((2*n+2)/3)} (2*n-2*k+1)!/(2*n-3*k+2)! * |Stirling1(n,k)|.

A377359 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x))/A(x) )^3.

Original entry on oeis.org

1, 3, 9, 57, 642, 9402, 177198, 4051338, 108926520, 3371293704, 118000461528, 4609447152120, 198791258476176, 9381618706074768, 480921576177145392, 26610634173004959312, 1580792845661466884352, 100345182367660427554560, 6778517964127816222982016
Offset: 0

Views

Author

Seiichi Manyama, Oct 26 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377350.
a(n) = 3 * Sum_{k=0..floor((3*n+3)/4)} (3*n-3*k+2)!/(3*n-4*k+3)! * |Stirling1(n,k)|.
Showing 1-5 of 5 results.