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 1-3 of 3 results.

A366356 G.f. satisfies A(x) = 1/(1 - x) + x/A(x).

Original entry on oeis.org

1, 2, -1, 6, -17, 71, -292, 1284, -5807, 26961, -127627, 613815, -2990680, 14730714, -73229290, 366936232, -1851352819, 9397497759, -47957377933, 245903408245, -1266266092111, 6545667052321, -33954266444497, 176689391245147, -922112642288148, 4825154135801698
Offset: 0

Views

Author

Seiichi Manyama, Oct 08 2023

Keywords

Links

Crossrefs

Partial sums give A363816.
Cf. A007317, A199475, A349289, A349290, A349291, A349292, A349293, A366357, A366358, A366359.
Cf. A112478, A366363.

Programs

  • Mathematica
    A366356[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[2k-1,n-k]/(2k-1),{k,0,n}];
Array[A366356,30,0] (* Paolo Xausa, Oct 20 2023 *)
  • PARI
    a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(2*k-1, n-k)/(2*k-1));

Formula

G.f.: A(x) = -2*x*(1-x) / (1-sqrt(1+4*x*(1-x)^2)).
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(2*k-1,n-k)/(2*k-1).

A363818 G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x)^2.

Original entry on oeis.org

1, 3, -1, 24, -125, 924, -6895, 54181, -438737, 3639655, -30769033, 264122781, -2296010693, 20171456222, -178818115155, 1597550237324, -14369097515939, 130010781029079, -1182520161325459, 10806114831458755, -99163805247182631, 913441732959868748
Offset: 0

Views

Author

Seiichi Manyama, Oct 18 2023

Keywords

Crossrefs

Cf. A162477, A363816, A364629, A364630.
Cf. A363819, A366364.

Programs

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

Formula

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

A363817 G.f. satisfies A(x) = (1 + x/A(x))/(1 - x)^3.

Original entry on oeis.org

1, 4, 5, 15, -5, 111, -402, 2172, -10892, 57362, -305756, 1656560, -9083341, 50328219, -281324174, 1584578882, -8984740332, 51242962422, -293772467974, 1691974930794, -9785378133066, 56805049768410, -330880419984556, 1933299689139664, -11328101469158229
Offset: 0

Views

Author

Seiichi Manyama, Oct 18 2023

Keywords

Crossrefs

Cf. A366363, A363816.

Programs

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

Formula

G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x)^3)).
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(3*(k-1),n-k)/(2*k-1).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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