A365694 -id:A365694 - cp's OEIS frontend

A365695 G.f. satisfies A(x) = 1 + x^3A(x)^5 / (1 - xA(x)).

1, 0, 0, 1, 1, 1, 6, 12, 19, 62, 156, 318, 852, 2254, 5262, 13441, 35543, 88772, 226880, 596937, 1539188, 3980364, 10468270, 27410289, 71702956, 189169352, 499529048, 1318355542, 3493861461, 9278408639, 24647900618, 65620808508, 175037591303, 467277998136

Offset: 0

Seiichi Manyama, Sep 16 2023

nonn

Cf. A023426, A023432, A054514, A114997, A365694.

a(n) = sum(k=0, n\3, binomial(n-2*k-1, n-3*k)*binomial(n+2*k+1, k)/(n+2*k+1));

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

A365723 G.f. satisfies A(x) = 1 + x^3A(x)^2(1 + x*A(x)).

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 2, 5, 3, 5, 21, 28, 26, 84, 180, 207, 385, 990, 1562, 2288, 5278, 10439, 15925, 30212, 64738, 112268, 192780, 396338, 761634, 1317840, 2512940, 5015867, 9146049, 16729462, 32927950, 62851525, 115101637, 220051350, 427898900, 800956600, 1505524800

Offset: 0

Seiichi Manyama, Sep 17 2023

nonn

Cf. A308616, A365724, A365725, A365726.

Cf. A365694.

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

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

cp's OEIS Frontend

A365695 G.f. satisfies A(x) = 1 + x^3A(x)^5 / (1 - xA(x)).

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A365723 G.f. satisfies A(x) = 1 + x^3A(x)^2(1 + x*A(x)).

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PARI

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cp's OEIS Frontend

A365695 G.f. satisfies A(x) = 1 + x^3*A(x)^5 / (1 - x*A(x)).

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Author

Keywords

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PARI

Formula

A365723 G.f. satisfies A(x) = 1 + x^3*A(x)^2*(1 + x*A(x)).

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Author

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PARI

Formula

A365695 G.f. satisfies A(x) = 1 + x^3A(x)^5 / (1 - xA(x)).

A365723 G.f. satisfies A(x) = 1 + x^3A(x)^2(1 + x*A(x)).