A360321 a(n) = Sum_{k=0..n} 5^(n-k) * binomial(n-1,n-k) * binomial(2*k,k).

1, 2, 16, 130, 1070, 8902, 74724, 631902, 5376840, 45990070, 395106656, 3407196982, 29477061166, 255733684010, 2224098916300, 19384492018770, 169270624419390, 1480625235653670, 12970844831940000, 113785067475668550, 999400688480388570

Offset

0,2

Links

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

Formula

G.f.: sqrt( (1-5*x)/(1-9*x) ).

n*a(n) = 2*(7*n-6)*a(n-1) - 45*(n-2)*a(n-2).

Sum_{i=0..n} Sum_{j=0..i} (1/5)^i * a(j) * a(i-j) = (9/5)^n.

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

Prog

(PARI) a(n) = sum(k=0, n, 5^(n-k)*binomial(n-1, n-k)*binomial(2*k, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-5*x)/(1-9*x)))

Crossrefs

Cf. A063886, A085362, A360317, A360318, A360319, A360322.

Sequence in context: A037720 A022018 A067684 * A074623 A323946 A275636

Adjacent sequences: A360318 A360319 A360320 * A360322 A360323 A360324

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2023

Status

approved