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 1-7 of 7 results.

A364623 G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^3.

Original entry on oeis.org

1, 4, 18, 112, 847, 7086, 62974, 583002, 5560323, 54249583, 538873135, 5431177821, 55402340842, 570899082760, 5933922697380, 62138800690564, 654949976467593, 6942859160218698, 73972792893687427, 791722414873487767, 8508265804914763731
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2023

Keywords

Crossrefs

Partial sums of A364629.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+5*k+2, 6*k+2)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+5*k+2,6*k+2) * binomial(3*k,k) / (2*k+1).

A364629 G.f. satisfies A(x) = (1+x*A(x)^3)/(1-x)^2.

Original entry on oeis.org

1, 3, 14, 94, 735, 6239, 55888, 520028, 4977321, 48689260, 484623552, 4892304686, 49971163021, 515496741918, 5363023614620, 56204877993184, 592811175777029, 6287909183751105, 67029933733468729, 717749621979800340, 7716543390041275964
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+5*k+1, 6*k+1)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+5*k+1,6*k+1) * binomial(3*k,k) / (2*k+1).

A364621 G.f. satisfies A(x) = 1/(1-x)^2 + x*A(x)^4.

Original entry on oeis.org

1, 3, 15, 118, 1125, 11805, 131431, 1524090, 18208749, 222570985, 2770129627, 34985756752, 447243818573, 5775955923428, 75245253495035, 987627627396792, 13048147674230169, 173382031819242855, 2315662483861709467, 31068798980975635130, 418552735866147739185
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+5*k+1, 6*k+1)*binomial(4*k, k)/(3*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+5*k+1,6*k+1) * binomial(4*k,k) / (3*k+1).

A366179 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x).

Original entry on oeis.org

1, 3, 13, 80, 582, 4627, 38906, 340138, 3060404, 28151835, 263546436, 2502686416, 24048985907, 233410500126, 2284790496700, 22530585455108, 223610524426654, 2231886642819974, 22389017726854323, 225604735477075272, 2282518274913713101
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2023

Keywords

Crossrefs

Partial sums of A366178.

Programs

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

Formula

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

A366180 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x)^3.

Original entry on oeis.org

1, 3, 15, 109, 909, 8184, 77626, 764226, 7735878, 80011063, 841875232, 8983175079, 96977392945, 1057262750608, 11623867926024, 128730566729686, 1434752590885174, 16080839356274157, 181135636330594960, 2049430159361529977, 23280997677471432102
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2023

Keywords

Crossrefs

Partial sums give A366182.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+6*k+1, n-k)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+6*k+1,n-k) * binomial(3*k,k)/(2*k+1).

A366177 G.f. A(x) satisfies A(x) = 1/(1 - x) + x*A(x)^3/(1 - x)^2.

Original entry on oeis.org

1, 2, 9, 55, 382, 2866, 22648, 185722, 1565725, 13486036, 118163960, 1049908872, 9437623630, 85671158757, 784247925911, 7231502249005, 67106161264660, 626221543735984, 5872908642398977, 55323451127462123, 523240983692525619, 4966658879361416551
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2023

Keywords

Crossrefs

Partial sums give A364620.

Programs

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

Formula

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

A366696 G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^3.

Original entry on oeis.org

1, 3, 10, 57, 378, 2730, 20853, 165592, 1353297, 11307168, 96148149, 829336122, 7238765532, 63816716547, 567425771478, 5082596905629, 45820260590481, 415423374916503, 3785371205061825, 34647928319586375, 318419608552433190, 2937021429784279707
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..n} binomial(2*(2*k+1),n-k) * binomial(3*k,k)/(2*k+1).
Showing 1-7 of 7 results.