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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A366454 G.f. A(x) satisfies A(x) = 1 + x + x/A(x)^(3/2).

Original entry on oeis.org

1, 2, -3, 12, -58, 312, -1794, 10794, -67113, 427800, -2780677, 18360504, -122809416, 830379966, -5666465445, 38974338126, -269915089194, 1880576960904, -13172489198859, 92705253700620, -655219698720486, 4648722344211012, -33096948925057703
Offset: 0

Views

Author

Seiichi Manyama, Oct 10 2023

Keywords

Crossrefs

Cf. A112478, A364393, A364407, A364408, A364409, A366266, A366267, A366268, A366452, A366453, A366455, A366456.
Cf. A366400.

Programs

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

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366400.
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(5*k/2-1,k) * binomial(n+3*k/2-2,n-k) / (5*k/2-1).

A378954 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^3/(1 + x*A(x)^2) )^2.

Original entry on oeis.org

1, 2, 11, 82, 705, 6584, 64902, 664608, 7001006, 75378082, 825810304, 9176278104, 103171720299, 1171558985630, 13416903518301, 154784357304138, 1797153050309355, 20984321920535966, 246252819129444579, 2902768234099178002, 34355158795966317996, 408086199665333171952
Offset: 0

Views

Author

Seiichi Manyama, Dec 12 2024

Keywords

Crossrefs

Cf. A364765, A378952.
Cf. A262441, A366400, A370474.

Programs

  • PARI
    a(n, r=2, s=-1, t=6, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Formula

G.f. A(x) satisfies:
(1) A(x) = 1/( 1 - x*A(x)^(5/2)/(1 + x*A(x)^2) )^2.
(2) A(x) = 1 + x * A(x)^2 * (1 + A(x)^(3/2)).
(3) A(x) = B(x)^2 where B(x) is the g.f. of A364765.
If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).
Previous Showing 11-12 of 12 results.

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

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