A366050 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x+x^2) ).

1, 3, 16, 104, 750, 5769, 46373, 384885, 3273118, 28372354, 249762585, 2226782078, 20065651123, 182457467898, 1672073116401, 15427427247088, 143191280370438, 1336062703751262, 12524930325385008, 117910257665608080, 1114233543986585741

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(4*n-k+2,n-2*k).

From Seiichi Manyama, Oct 08 2025: (Start)

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

a(n) = (1/(n+1)) * [x^n] ((1-x+x^2) / (1-x)^4)^(n+1). (End)

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(4*n-k+2, n-2*k))/(n+1);

Crossrefs

Cf. A005043, A109081, A366049.

Sequence in context: A365752 A207434 A074542 * A368934 A344216 A393734

Adjacent sequences: A366047 A366048 A366049 * A366051 A366052 A366053

Keyword

nonn

Author

Seiichi Manyama, Sep 27 2023

Status

approved