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 A370172 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^2)^3 )^n. 3
 1, 5, 51, 581, 6963, 85905, 1079943, 13756216, 176939187, 2292988919, 29892396451, 391576960230, 5150057095527, 67962810381653, 899458144305408, 11933576896320981, 158672857603511987, 2113800649819533735, 28207266176359605705, 376976971371883606824 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..19. FORMULA 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. PROG (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)); CROSSREFS Cf. A370170, A370171. Cf. A369480. Sequence in context: A041040 A088320 A223002 * A180511 A245926 A190734 Adjacent sequences: A370169 A370170 A370171 * A370173 A370174 A370175 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 11 2024 STATUS approved

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Last modified August 8 16:21 EDT 2024. Contains 375023 sequences. (Running on oeis4.)