A365609 G.f. satisfies A(x) = 1 + x^2*A(x)^4*(1 + x*A(x)).

1, 0, 1, 1, 4, 9, 27, 78, 231, 715, 2193, 6954, 21999, 70840, 228896, 746650, 2447757, 8072208, 26745627, 89002364, 297344960, 996865397, 3352918429, 11310307593, 38256171642, 129718262583, 440855654827, 1501451066767, 5123671576890, 17516503865294

Offset

0,5

Links

Table of n, a(n) for n=0..29.

Formula

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

Prog

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

Crossrefs

Cf. A001005, A025250, A055113, A217358.

Cf. A365690.

Sequence in context: A329155 A111962 A307528 * A198095 A256096 A071913

Adjacent sequences: A365606 A365607 A365608 * A365610 A365611 A365612

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved