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 1-10 of 18 results. Next

A366266 G.f. A(x) satisfies A(x) = 1 + x + x*A(x)^3.

Original entry on oeis.org

1, 2, 6, 30, 170, 1050, 6846, 46374, 323154, 2301618, 16680246, 122607342, 911868282, 6849381194, 51885977838, 395941193718, 3040818657954, 23485437201762, 182297207394150, 1421357996034750, 11126867651367498, 87421958424703098, 689130671539597854
Offset: 0

Views

Author

Seiichi Manyama, Oct 06 2023

Keywords

Crossrefs

Cf. A025227, A366267, A366268.
Cf. A366221, A366364.

Programs

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

Formula

a(n) = Sum_{k=0..n} binomial(2*k+1,n-k) * binomial(3*k,k)/(2*k+1).
a(n) = A366221(n) + A366221(n-1).
G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366364.

A366272 G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^3*A(x)^4.

Original entry on oeis.org

1, 1, 7, 49, 399, 3521, 32767, 316673, 3147775, 31977985, 330544639, 3465369601, 36759599103, 393820102657, 4255079743487, 46313023946753, 507319247208447, 5588706552643585, 61875364144283647, 688128167799619585, 7683686768042639359
Offset: 0

Views

Author

Seiichi Manyama, Oct 06 2023

Keywords

Crossrefs

Cf. A052709, A366221, A366273.
Cf. A366267, A366436.

Programs

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

Formula

a(n) = Sum_{k=0..n} binomial(3*k,n-k) * binomial(4*k,k)/(3*k+1).
G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366436.

A366273 G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^4*A(x)^5.

Original entry on oeis.org

1, 1, 9, 81, 849, 9681, 116601, 1459809, 18809121, 247782369, 3322209001, 45187029809, 621970864241, 8647376531249, 121261376439641, 1713085987837889, 24358211622230081, 348325689458584769, 5006342381846708681, 72279683684984063249, 1047789195353379807121
Offset: 0

Views

Author

Seiichi Manyama, Oct 06 2023

Keywords

Crossrefs

Cf. A052709, A366221, A366272.
Cf. A366268.

Programs

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

Formula

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

A366495 G.f. A(x) satisfies A(x) = 1 + x*(1+x)^(3/2)*A(x)^(5/2).

Original entry on oeis.org

1, 1, 4, 16, 74, 366, 1900, 10210, 56315, 317005, 1813860, 10518652, 61684208, 365177622, 2179549853, 13100686947, 79232836206, 481821573994, 2944253855746, 18069720545174, 111333779015326, 688399685561554, 4270250156814421, 26567075153764929
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366496, A366497, A366498, A366499, A366500, A366501.
Cf. A366433.

Programs

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

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366433.
a(n) = Sum_{k=0..n} binomial(3*k/2,n-k) * binomial(5*k/2,k) / (3*k/2+1).

A366496 G.f. A(x) satisfies A(x) = 1 + x*(1+x)^(5/2)*A(x)^(7/2).

Original entry on oeis.org

1, 1, 6, 36, 251, 1891, 15007, 123593, 1046444, 9052330, 79660406, 710879890, 6418000050, 58515227946, 538008396198, 4982752630656, 46442071874398, 435299781856712, 4100411743983559, 38797120485576155, 368561495153257186, 3513923237883474314
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366497, A366498, A366499, A366500, A366501.
Cf. A366435.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(5*k/2, n-k)*binomial(7*k/2, k)/(5*k/2+1));

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366435.
a(n) = Sum_{k=0..n} binomial(5*k/2,n-k) * binomial(7*k/2,k) / (5*k/2+1).

A366497 G.f. A(x) satisfies A(x) = 1 + x*(1+x)^(7/2)*A(x)^(9/2).

Original entry on oeis.org

1, 1, 8, 64, 596, 6028, 64352, 713812, 8146490, 95040886, 1128369960, 13588883712, 165598378308, 2038279921692, 25303322898120, 316443054086214, 3983011314348183, 50418720131975193, 641444450506307160, 8197477211343267688, 105185927879224420064
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366498, A366499, A366500, A366501.
Cf. A366437.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(7*k/2, n-k)*binomial(9*k/2, k)/(7*k/2+1));

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366437.
a(n) = Sum_{k=0..n} binomial(7*k/2,n-k) * binomial(9*k/2,k) / (7*k/2+1).

A366498 G.f. A(x) satisfies A(x) = 1 + x / ((1+x)^(5/2)*A(x)^(3/2)).

Original entry on oeis.org

1, 1, -4, 16, -74, 386, -2180, 12974, -80087, 507887, -3288564, 21649068, -144458484, 974838450, -6641303895, 45615642021, -315530731215, 2196107692119, -15368596890978, 108073850591598, -763293549312084, 5412015893523096, -38508964818580799
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366497, A366499, A366500, A366501.
Cf. A366431.

Programs

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

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366431.
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(n+3*k/2-1,n-k) * binomial(5*k/2-1,k) / (5*k/2-1).

A366499 G.f. A(x) satisfies A(x) = 1 + x / ((1+x)^3*A(x)^2).

Original entry on oeis.org

1, 1, -5, 25, -145, 945, -6641, 49057, -375361, 2948353, -23634049, 192554753, -1589812225, 13272519937, -111850866433, 950220134913, -8129133081601, 69971682467841, -605546841831425, 5265763716550657, -45988028107350017, 403192288488677377
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366497, A366498, A366500, A366501.
Cf. A213282.

Programs

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

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A213282.
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(n+2*k-1,n-k) * binomial(3*k-1,k) / (3*k-1).

A366500 G.f. A(x) satisfies A(x) = 1 + x / ((1+x)^(7/2)*A(x)^(5/2)).

Original entry on oeis.org

1, 1, -6, 36, -251, 1961, -16477, 145307, -1326227, 12420057, -118666032, 1152120806, -11333969511, 112728949041, -1131701419316, 11452480598696, -116702578057106, 1196469605151736, -12332629378843566, 127727907921601146, -1328542834131885506
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366497, A366498, A366499, A366501.
Cf. A366432.

Programs

  • PARI
    a(n) = (-1)^(n-1)*sum(k=0, n, binomial(n+5*k/2-1, n-k)*binomial(7*k/2-1, k)/(7*k/2-1));

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366432.
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(n+5*k/2-1,n-k) * binomial(7*k/2-1,k) / (7*k/2-1).

A366501 G.f. A(x) satisfies A(x) = 1 + x / ((1+x)^4*A(x)^3).

Original entry on oeis.org

1, 1, -7, 49, -399, 3633, -35511, 363937, -3858079, 41951521, -465296487, 5243459409, -59865074223, 690979478481, -8049598938135, 94522387901505, -1117615459764031, 13294669980012865, -158995530738069703, 1910555096402418545, -23056131790988675279
Offset: 0

Views

Author

Seiichi Manyama, Oct 11 2023

Keywords

Crossrefs

Cf. A001006, A366221, A366272, A366273, A366495, A366496, A366497, A366498, A366499, A366500.
Cf. A213336.

Programs

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

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A213336.
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(n+3*k-1,n-k) * binomial(4*k-1,k) / (4*k-1).
Showing 1-10 of 18 results. Next

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