A370247 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^3) )^n.
1, 2, 10, 59, 362, 2277, 14575, 94474, 618154, 4074197, 27008885, 179897720, 1202961215, 8070830588, 54302131642, 366252974259, 2475575739306, 16764524795037, 113719280941453, 772551326290528, 5255393538550837, 35794109754866998, 244060675562790316
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*n-3*k-1,n-3*k).
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 A369265.