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a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(3*n,n-k).
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%I #9 Feb 10 2024 09:23:42

%S 1,1,-3,-17,-19,126,591,344,-5907,-22373,2122,280842,854063,-810692,

%T -13254552,-31693392,67250413,615932985,1101123015,-4368359919,

%U -28043889894,-33371056204,254637122506,1245324193704,693586015791,-13913192640499

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

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

%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x/((1-x)^2*(1+x)^3) ). See A370107.

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

%Y Cf. A234839, A368467.

%Y Cf. A370107.

%K sign

%O 0,3

%A _Seiichi Manyama_, Feb 10 2024