A086629 -id:A086629 - cp's OEIS frontend

A086631 Antidiagonal sums of square table A086629.

1, 2, 4, 10, 29, 92, 310, 1088, 3931, 14518, 54551, 207856, 801202, 3118532, 12239732, 48385852, 192483953, 769974110, 3095236066, 12497442266, 50660112478, 206093561590, 841151382755, 3443278744832, 14133534466258

Offset: 0

Paul D. Hanna, Jul 24 2003

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A001764, A086615, A086629 (table), A086630 (diagonal).

a(n) = sum(k=0, n\2, binomial(n+2*k+1, 4*k+1)*binomial(3*k, k)/(2*k+1)); \\ Seiichi Manyama, Jul 30 2023

G.f.: A(x) = 1/(1-x)^2 + x^2*A(x)^3.

a(n) = Sum_{k=0..floor(n/2)} binomial(n+2*k+1,4*k+1) * binomial(3*k,k) / (2*k+1). - Seiichi Manyama, Jul 30 2023

A086630 Main diagonal of square table A086629; coefficients of x^ny^n in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xyf(x,y)^3.

Original entry on oeis.org

1, 2, 13, 124, 1419, 18037, 245650, 3513260, 52114339, 795230788, 12411836882, 197327486617, 3185686181794, 52101500060794, 861628197679360

Offset: 0

Paul D. Hanna, Jul 24 2003

nonn

Cf. A086629 (table), A086631 (antidiagonal sums).

cp's OEIS Frontend

A086631 Antidiagonal sums of square table A086629.

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A086630 Main diagonal of square table A086629; coefficients of x^ny^n in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xyf(x,y)^3.

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Author

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cp's OEIS Frontend

A086631 Antidiagonal sums of square table A086629.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A086630 Main diagonal of square table A086629; coefficients of x^n*y^n in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xy*f(x,y)^3.

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Author

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A086630 Main diagonal of square table A086629; coefficients of x^ny^n in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xyf(x,y)^3.