A370286 Coefficient of x^n in the expansion of ( (1+x)^3 + x^2 )^n.
1, 3, 17, 102, 645, 4193, 27764, 186231, 1261213, 8604759, 59053167, 407217396, 2819252544, 19583729766, 136426565999, 952743556907, 6667916884701, 46755146944959, 328398159653117, 2310073990369926, 16271915501598595, 114757849228310355
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, binomial(n, k)*binomial(3*n-3*k, n-2*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(3*n-3*k,n-2*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)^3 + x^2) ).