A360319 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n-1,n-k) * binomial(2*k,k).

1, 2, 14, 100, 726, 5340, 39692, 297544, 2245990, 17050796, 130061412, 996078456, 7654571772, 58995989400, 455857911768, 3530234227344, 27392392806534, 212918339726028, 1657570714812020, 12922254685161112, 100867892292766612

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: sqrt( (1-4*x)/(1-8*x) ).

n*a(n) = 2*(6*n-5)*a(n-1) - 32*(n-2)*a(n-2).

Sum_{i=0..n} Sum_{j=0..i} (1/4)^i * a(j) * a(i-j) = 2^n.

a(n) ~ 2^(3*n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 04 2023

Prog

(PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(n-1, n-k)*binomial(2*k, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-4*x)/(1-8*x)))

Crossrefs

Cf. A063886, A085362, A360317, A360318, A360321, A360322.

Sequence in context: A037719 A158811 A198280 * A074620 A185010 A144277

Adjacent sequences: A360316 A360317 A360318 * A360320 A360321 A360322

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2023

Status

approved