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
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Oct 10 2018
STATUS
approved