A365765 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x) ).

1, 5, 39, 365, 3772, 41491, 476410, 5644477, 68493324, 846937140, 10633195119, 135185288475, 1736883987836, 22516798984946, 294169295918996, 3869084306851933, 51189853304834940, 680816769653570044, 9097058255214149068, 122064057533865334100

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..865

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(5*n-k+3,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(n+1,n-k).

Prog

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

Crossrefs

Cf. A003169, A006318, A365764, A365766.

Cf. A365752.

Sequence in context: A213233 A115187 A266456 * A247772 A129763 A277424

Adjacent sequences: A365762 A365763 A365764 * A365766 A365767 A365768

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved