A395706 Expansion of g^6*(4*g-3)/(5-4*g)^4, where g = 1+x*g^5 is the g.f. of A002294.

1, 26, 489, 8084, 124650, 1839930, 26358136, 369456808, 5093456427, 69310704900, 933297754070, 12458823064980, 165112564733584, 2174713789595312, 28491597935859600, 371556637135174480, 4825834052057950585, 62454257295069085470, 805682563120975717799, 10363864582375153958600

Offset

0,2

Links

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

Formula

a(n) = (n+1) * A386367(n+1).

G.f.: (Sum_{k>=0} (8*k+3)/(5*k+3) * binomial(5*k+3,k) * x^k) * (Sum_{k>=0} binomial(5*k,k) * x^k)^3.

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

a(n) = (n+1) * Sum_{k=0..n} binomial(5*k+3+l,k) * binomial(5*n-5*k-l,n-k) for every real number l.

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

a(n) = (n+1) * Sum_{k=0..n} 5^(n-k) * binomial(4*n+k+3,k).

Prog

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

Crossrefs

Cf. A395704, A395705, A395707.

Cf. A002294, A386367, A395665.

Sequence in context: A240190 A001723 A163201 * A395703 A205990 A230247

Adjacent sequences: A395703 A395704 A395705 * A395707 A395708 A395709

Keyword

nonn

Author

Seiichi Manyama, May 04 2026

Status

approved