A371787 - OEIS

%I #12 Jun 05 2024 04:25:07

%S 1,5,44,441,4675,51129,570401,6451688,73715212,848793726,9833394285,

%T 114487194485,1338411363535,15700659542105,184722993467063,

%U 2178831068873601,25756348168285379,305061478075705411,3619402085862708614,43008294559624639777

%N a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(5*n-k,n-2*k).

%F a(n) = [x^n] 1/((1-x+x^2) * (1-x)^(4*n)).

%F It appears that a(n) = Sum_{k = 0..n} binomial(3*n+2*k-1, k). - _Peter Bala_, Jun 04 2024

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(5*n-k, n-2*k));

%Y Cf. A024718, A371785, A371786.

%Y Cf. A371744.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Apr 06 2024