A370106 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(3*n,n-k).
1, 1, -3, -17, -19, 126, 591, 344, -5907, -22373, 2122, 280842, 854063, -810692, -13254552, -31693392, 67250413, 615932985, 1101123015, -4368359919, -28043889894, -33371056204, 254637122506, 1245324193704, 693586015791, -13913192640499
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-1)^k * binomial(2*n, k)*binomial(3*n, n-k));
Formula
a(n) = [x^n] ( (1-x)^2 * (1+x)^3 )^n.
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.