A320326 a(n) = Sum_{i=0..n} binomial(2*i-1,i)*binomial(2*i,n-i).

1, 1, 5, 23, 113, 568, 2905, 15040, 78581, 413496, 2188204, 11633666, 62089785, 332459890, 1785132500, 9608402738, 51826221461, 280063787170, 1515943655628, 8217729019538, 44606550971500, 242419877520384, 1318902900434870

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: (2*x^3 + 4*x^2 + 2*x)/(sqrt(-4*x^3 - 8*x^2 - 4*x + 1) + 4*x^3 + 8*x^2 + 4*x - 1).

Recurrence: n*a(n) = 2*(2*n - 1)*a(n-1) + 8*(n-1)*a(n-2) + 2*(2*n - 3)*a(n-3). - Vaclav Kotesovec, Oct 11 2018

Maple

a:=n->add(binomial(2*i-1, i)*binomial(2*i, n-i), i=0..n): seq(a(n), n=0..25); # Muniru A Asiru, Oct 11 2018

Mathematica

Table[Sum[Binomial[2*i - 1, i]*Binomial[2*i, n - i], {i, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Oct 11 2018 *)

Prog

(GAP) List([0..25], n->Sum([0..n], i->Binomial(2*i-1, i)*Binomial(2*i, n-i))); # Muniru A Asiru, Oct 11 2018
(PARI) a(n) = sum(i=0, n, binomial(2*i-1, i)*binomial(2*i, n-i)); \\ Michel Marcus, Oct 11 2018

Crossrefs

Cf. A001700.

Sequence in context: A178873 A186652 A199312 * A299589 A113284 A104090

Adjacent sequences: A320323 A320324 A320325 * A320327 A320328 A320329

Keyword

nonn

Author

Vladimir Kruchinin, Oct 10 2018

Status

approved