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 1-2 of 2 results.

A372013 G.f. A(x) satisfies A(x) = 1/( 1 + x*(1 - 9*x*A(x))^(1/3) ).

Original entry on oeis.org

1, -1, 4, -1, 46, 149, 1351, 8441, 63499, 462752, 3514807, 26923478, 209566927, 1647633779, 13079663527, 104649229988, 843120766711, 6833665175513, 55683581174641, 455878084448132, 3748025535972448, 30931714278955736, 256150668109462507
Offset: 0

Views

Author

Seiichi Manyama, Apr 19 2024

Keywords

Crossrefs

Cf. A166587, A362155, A372012.

Programs

  • PARI
    a(n) = (-1)^n*sum(k=0, n, 9^(n-k)*binomial(n, k)*binomial(k/3, n-k)/(n-k+1));

Formula

a(n) = (-1)^n * Sum_{k=0..n} 9^(n-k) * binomial(n,k) * binomial(k/3,n-k)/(n-k+1).

A372125 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)*(1 + 4*x*A(x))^(1/2) ).

Original entry on oeis.org

1, 1, 4, 13, 60, 256, 1252, 5979, 30360, 153626, 801632, 4197284, 22355788, 119695396, 647666544, 3522773337, 19298660772, 106213538104, 587632185580, 3264011196578, 18203515158400, 101862717712340, 571859834176800, 3219573318768300, 18175140989890716
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2024

Keywords

Links

Crossrefs

Cf. A001002, A372126.
Cf. A372012, A378554.

Programs

  • PARI
    a(n) = sum(k=0, n, 4^(n-k)*binomial(n+k, k)*binomial(k/2, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 4^(n-k) * binomial(n+k,k) * binomial(k/2,n-k).
From Seiichi Manyama, Nov 30 2024: (Start)
G.f.: exp( Sum_{k>=1} A378554(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] 1/(1 - x*(1 + 4*x)^(1/2))^(n+1).
G.f.: (1/x) * Series_Reversion( x*(1 - x*(1 + 4*x)^(1/2)) ). (End)
Showing 1-2 of 2 results.

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

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