A365725 G.f. satisfies A(x) = 1 + x^3*A(x)^4*(1 + x*A(x)).

1, 0, 0, 1, 1, 0, 4, 9, 5, 22, 78, 91, 175, 680, 1224, 1938, 6270, 14630, 24794, 63756, 166980, 322920, 720720, 1900080, 4125888, 8803008, 22151360, 51778804, 111882100, 267682272, 645736432, 1442390092, 3346519020, 8094247798, 18657762006, 42890295734

Offset: 0

Author

Seiichi Manyama, Sep 17 2023

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A308616, A365723, A365724, A365726.

Cf. A001002, A217358, A365731.

Cf. A054514.

Programs

PARI

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

Formula

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

G.f.: (1/x) * Series_Reversion( x*(1 - x^3*(1 + x)) ). - Seiichi Manyama, Sep 24 2024