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 1-6 of 6 results.

A366184 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3)/(1 - x)^3.

Original entry on oeis.org

1, 4, 21, 163, 1487, 14697, 153226, 1659338, 18483960, 210437161, 2437721418, 28640748192, 340473075541, 4087735789616, 49494986770104, 603699827411356, 7410709463933414, 91484338902961485, 1135029142529785303, 14145212892466682781, 176993823220824229047
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+8*k+2, n-k)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+8*k+2,n-k) * binomial(3*k,k)/(2*k+1).

A366182 G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*A(x)^3/(1 - x).

Original entry on oeis.org

1, 4, 19, 128, 1037, 9221, 86847, 851073, 8586951, 88598014, 930473246, 9913648325, 106891041270, 1164153791878, 12788021717902, 141518588447588, 1576271179332762, 17657110535606919, 198792746866201879, 2248222906227731856, 25529220583699163958
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2023

Keywords

Crossrefs

Partial sums of A366180.

Programs

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

Formula

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

A364624 G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^4.

Original entry on oeis.org

1, 4, 22, 194, 2103, 25129, 318816, 4214724, 57419725, 800461033, 11363418314, 163708299724, 2387365301187, 35173224652637, 522752043513952, 7827979832083872, 117992516684761733, 1788819120580964014, 27258417705055812586, 417270970443908301926
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+8*k+2, 9*k+2)*binomial(4*k, k)/(3*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+8*k+2,9*k+2) * binomial(4*k,k) / (3*k+1).

A366183 G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*A(x)^3/(1 - x)^2.

Original entry on oeis.org

1, 4, 20, 145, 1250, 11746, 116641, 1204039, 12790067, 138895021, 1535005454, 17207743738, 195197256289, 2236419124408, 25842382083071, 300822398531482, 3524358836945936, 41524956284752018, 491722951928324392, 5848997420625891294, 69854562522309219081
Offset: 0

Views

Author

Seiichi Manyama, Oct 03 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+7*k+2, n-k)*binomial(3*k, k)/(2*k+1));

Formula

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

A366697 G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^3.

Original entry on oeis.org

1, 4, 15, 94, 706, 5769, 49923, 449376, 4164228, 39459852, 380594767, 3724049805, 36876008673, 368835076813, 3720863181033, 37815675159285, 386818379566749, 3979362306753315, 41144521893563511, 427335033811660713, 4456402044181677264
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Programs

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

Formula

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

A369691 G.f. satisfies A(x) = 1/(1-x)^3 + x^3*A(x)^3.

Original entry on oeis.org

1, 3, 6, 11, 24, 66, 196, 576, 1692, 5110, 15933, 50604, 161988, 521700, 1693362, 5541679, 18260055, 60487659, 201272437, 672550158, 2256204327, 7596059333, 25655943417, 86904524289, 295154911774, 1004906765178, 3429178160346, 11726499288028, 40178538608682
Offset: 0

Views

Author

Seiichi Manyama, Jan 29 2024

Keywords

Crossrefs

Programs

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

Formula

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