A387840 Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1-x+x^2) ).

1, 4, 27, 221, 2004, 19370, 195584, 2038664, 21770217, 236941760, 2618720692, 29311169343, 331577919891, 3784930267188, 43541666412459, 504299421731877, 5875568109960575, 68816531233181276, 809783886875736683, 9569059083207116356, 113504808314574441720

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(5*n-k+3,n-2*k).

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

a(n) = (1/(n+1)) * [x^n] ((1-x+x^2) / (1-x)^5)^(n+1).

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(5*n-k+3, n-2*k))/(n+1);

Crossrefs

Cf. A005043, A109081, A366049, A366050.

Sequence in context: A304045 A365753 A317103 * A381880 A341962 A354588

Adjacent sequences: A387837 A387838 A387839 * A387841 A387842 A387843

Keyword

nonn

Author

Seiichi Manyama, Oct 08 2025

Status

approved