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 A370273 Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3) )^n. 1
 1, 2, 10, 59, 362, 2277, 14581, 94572, 619242, 4084538, 27099435, 180651913, 1209036725, 8118629365, 54671662692, 369071775684, 2496852123882, 16923762715911, 114902801532622, 781296976824693, 5319705042364587, 36265061394634215, 247497082392976415 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..22. FORMULA a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,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 A369297. PROG (PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k)); CROSSREFS Cf. A369297. Sequence in context: A026132 A226996 A370247 * A309955 A340987 A186758 Adjacent sequences: A370270 A370271 A370272 * A370274 A370275 A370276 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 13 2024 STATUS approved

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)