A390687 - OEIS

%I #11 Nov 15 2025 07:53:39

%S 1,4,27,210,1730,14704,127470,1120262,9944676,88961008,800658947,

%T 7241596046,65764261576,599284477328,5477020329872,50182223592510,

%U 460796527028636,4239427396585840,39070459427293260,360622779428966656,3333138696913131830,30845466968858253248

%N a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-2*k,n-2*k).

%H Seiichi Manyama, <a href="/A390687/b390687.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = [x^n] 1/((1+x^2) * (1-x)^(3*n+1)).

%F a(n) = Sum_{k=0..n} (-2)^k * binomial(4*n+k+2,n-k).

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k, n-2*k));

%Y Cf. A176332, A390686.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 15 2025