A395665 Expansion of g^6/(5-4*g)^4, where g = 1+x*g^5 is the g.f. of A002294.

1, 22, 381, 5980, 88890, 1276230, 17886232, 246252152, 3344275035, 44927630620, 598267799470, 7908642146460, 103903677936656, 1357912154470480, 17665817998003920, 228911472376400880, 2955823973420033945, 38048495304410020530, 488413557020228804275, 6253899031995196345240

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: (Sum_{k>=0} binomial(5*k+2,k) * x^k) * (Sum_{k>=0} binomial(5*k,k) * x^k)^3.

Sum_{k>=1} a(k-1) * x^k/k^2 = (1/10) * log( Sum_{k>=0} binomial(5*k+5,k) * x^k ).

a(n) = ((n+1)/10) * (binomial(5*n+4,n) + Sum_{k=0..n+1} 4^(n+1-k) * binomial(5*n+5,k)).

a(n) = ((n+1)/8) * Sum_{k=0..n+1} 4^(n+1-k) * binomial(5*n+4,k).

a(n) = Sum_{k=0..n} 4^k * binomial(k+2,2) * binomial(5*n+5,n-k).

Prog

(PARI) a(n) = (n+1)*(binomial(5*n+4, n)+sum(k=0, n+1, 4^(n+1-k)*binomial(5*n+5, k)))/10;

Crossrefs

Cf. A378504, A394853, A395664, A395667, A395675.

Cf. A002294, A004343, A395668.

Sequence in context: A132167 A167033 A222886 * A264464 A268947 A159761

Adjacent sequences: A395662 A395663 A395664 * A395667 A395668 A395669

Keyword

nonn

Author

Seiichi Manyama, May 03 2026

Status

approved