A390686 - OEIS

%I #11 Nov 15 2025 07:52:49

%S 1,3,14,77,451,2728,16834,105317,665551,4238463,27156744,174858972,

%T 1130494236,7333934988,47717158394,311248100517,2034664811631,

%U 13326556644753,87435235471214,574537592170357,3780472550923091,24906432444097408,164272522873515704

%N a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n-2*k,n-2*k).

%H Seiichi Manyama, <a href="/A390686/b390686.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = Sum_{k=0..n} (-2)^k * binomial(3*n+k+2,n-k).

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(3*n-2*k, n-2*k));

%Y Cf. A176332, A390687.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 15 2025