A372006 G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)*(1 + x*A(x)) )^(1/5).

1, 5, -20, 100, 0, -9625, 169875, -1933125, 14025625, 0, -2065744375, 41575056250, -523670743750, 4119815531250, 0, -684944792812500, 14442398472421875, -189324209836328125, 1541918426557031250, 0, -271410262779871875000, 5860693797318871093750

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 25^k * binomial(n/5+1/5,k) * binomial(k,n-k).

a(5*n+4) = 0 for n >= 0.

a(n) = 25^n*binomial((n+1)/5, n)*hypergeom([(1-n)/2, -n/2], [(6-4*n)/5], 4/25)/(n+1). - Stefano Spezia, Apr 18 2024

Prog

(PARI) a(n) = sum(k=0, n, 25^k*binomial(n/5+1/5, k)*binomial(k, n-k))/(n+1);

Crossrefs

Cf. A372004, A372005.

Sequence in context: A357786 A020046 A319731 * A272218 A026118 A108509

Adjacent sequences: A372003 A372004 A372005 * A372008 A372010 A372012

Keyword

sign,changed

Author

Seiichi Manyama, Apr 15 2024

Status

approved