A378403 - OEIS

%I #6 Nov 25 2024 09:07:41

%S 1,2,10,53,290,1632,9349,54231,317538,1872800,11109520,66213215,

%T 396181229,2378362248,14318234311,86409741438,522592913026,

%U 3166515425796,19218755044816,116820035092706,711037336745440,4333057549362840,26434747722608191,161433098212966732

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

%F a(n) = [x^n] (1 + x + x * (1 + x)^3)^n.

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

%Y Cf. A000984, A082759, A378404.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 25 2024