A378611 - OEIS

%I #12 Dec 02 2024 10:09:37

%S 1,2,14,104,806,6412,51908,425476,3520070,29332940,245841284,

%T 2070093632,17499188924,148414157816,1262280506144,10762045739644,

%U 91951462167110,787113739061260,6749009521216052,57954807274992208,498334047795436276,4290199618047230824

%N a(n) = Sum_{k=0..n} binomial(2*n+k-1,k) * binomial(n-1,n-k).

%F a(n) = [x^n] 1/(1 - x/(1 - x))^(2*n).

%F a(n) = (1/2)^n * [x^(2*n)] 2/(1 - x/(1 - x))^n for n > 0.

%F a(n) = 2 * A259554(n) for n > 0.

%o (PARI) a(n) = sum(k=0, n, binomial(2*n+k-1, k)*binomial(n-1, n-k));

%Y Cf. A002002, A378612, A378613.

%Y Cf. A211789, A259554.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 01 2024