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Expansion of 1/(1 - 4*x^2 - 4*x^3)^(3/2).
3

%I #10 Oct 19 2024 08:31:52

%S 1,0,6,6,30,60,170,420,1050,2660,6552,16380,40362,99792,245520,603372,

%T 1480050,3624192,8863712,21647340,52811616,128700000,313341756,

%U 762206016,1852565650,4499346072,10919990460,26485897932,64201490352,155536089240,376606931436

%N Expansion of 1/(1 - 4*x^2 - 4*x^3)^(3/2).

%F a(0) = 1, a(1) = 0, a(2) = 6; a(n) = (4*(n+1)*a(n-2) + 2*(2*n+3)*a(n-3))/n.

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

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

%Y Cf. A115962, A377189, A377190.

%Y Cf. A374497.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 19 2024