A372005 G.f. A(x) satisfies A(x) = ( 1 + 16*x*A(x)*(1 + x*A(x)) )^(1/4).

1, 4, -4, 0, 136, -1152, 5152, 0, -230560, 2267136, -11355008, 0, 594412800, -6184304640, 32458736640, 0, -1828185954816, 19583341166592, -105435193825280, 0, 6195266435870720, -67554137604096000, 369569533686562816, 0, -22322916873246359552, 246346071588005216256

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 16^k * binomial(n/4+1/4,k) * binomial(k,n-k).

a(4*n+3) = 0 for n >= 0.

a(n) = 16^n*binomial((n+1)/4, n)*hypergeom([(1-n)/2, -n/2], [(5-3*n)/4], 1/4)/(n+1). - Stefano Spezia, Apr 18 2024

Prog

(PARI) a(n) = sum(k=0, n, 16^k*binomial(n/4+1/4, k)*binomial(k, n-k))/(n+1);

Crossrefs

Cf. A372004, A372006.

Sequence in context: A111848 A204384 A102412 * A350491 A365957 A365954

Adjacent sequences: A372002 A372003 A372004 * A372006 A372008 A372010

Keyword

sign

Author

Seiichi Manyama, Apr 15 2024

Status

approved