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%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
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