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.

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A365087 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^4.

Original entry on oeis.org

1, 1, -3, -1, 29, -44, -265, 1114, 1369, -19076, 20388, 250977, -875281, -2116594, 19136754, -7765108, -306092007, 830209808, 3388957208, -22266676364, -8185922076, 413223401045, -814031607979, -5513566634947, 27558060911119, 35395095404776
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2023

Keywords

Crossrefs

Cf. A090192, A365085, A365086, A365088.
Cf. A321798, A364737, A365083.

Programs

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

Formula

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

A365084 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x)^5.

Original entry on oeis.org

1, 1, -4, 6, 6, -49, 95, 24, -592, 1417, -414, -6809, 20142, -14831, -73353, 274761, -311105, -715647, 3607624, -5463428, -5785294, 45588556, -87189477, -25565196, 552659892, -1305250324, 340413165, 6379267117, -18606431142, 13202513476, 69064770845
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2023

Keywords

Links

Crossrefs

Cf. A106510, A127896, A365083.
Cf. A079675.

Programs

  • Mathematica
    LinearRecurrence[{-4, -10, -10, -5, -1}, {1, 1, -4, 6, 6, -49}, 1 + 30] (* Robert P. P. McKone, Aug 21 2023 *)
  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+4*k-1, n-k));

Formula

G.f.: A(x) = 1/( 1 - x/(1+x)^5 ).
a(n) = -4*a(n-1) - 10*a(n-2) - 10*a(n-3) - 5*a(n-4) - a(n-5) for n > 5.
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+4*k-1,n-k).
Showing 1-2 of 2 results.

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

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