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A370172
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Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^2)^3 )^n.
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3
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1, 5, 51, 581, 6963, 85905, 1079943, 13756216, 176939187, 2292988919, 29892396451, 391576960230, 5150057095527, 67962810381653, 899458144305408, 11933576896320981, 158672857603511987, 2113800649819533735, 28207266176359605705, 376976971371883606824
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(5*n-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)^2 * (1+x+x^2)^3) ). See A369480.
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PROG
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(PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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