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 A303906 Expansion of Product_{k>=2} 1/(1 - x^(k*(k+1)/2)). 2
 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 3, 1, 0, 4, 2, 0, 5, 2, 1, 7, 3, 1, 8, 4, 2, 10, 6, 2, 13, 8, 3, 15, 10, 4, 20, 12, 6, 22, 16, 8, 28, 19, 10, 33, 25, 12, 40, 29, 16, 48, 36, 19, 55, 44, 26, 65, 53, 30, 76, 64, 38, 88, 75, 46, 106, 88, 56, 119, 105, 68, 141, 122, 80, 160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS First differences of A007294. Number of partitions of n into triangular numbers > 1. LINKS FORMULA G.f.: 1 + Sum_{j>=2} x^(j*(j+1)/2)/Product_{k=2..j} (1 - x^(k*(k+1)/2)). a(n) ~ exp(3 * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3) / 2) * Zeta(3/2)^(5/3) / (2^(9/2) * sqrt(3) * Pi^(2/3) * n^(13/6)). - Vaclav Kotesovec, May 04 2018 MATHEMATICA nmax = 75; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)/2)), {k, 2, nmax}], {x, 0, nmax}], x] nmax = 75; CoefficientList[Series[1 + Sum[x^(j (j + 1)/2)/Product[(1 - x^(k (k + 1)/2)), {k, 2, j}], {j, 2, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A000217, A002865, A007294, A078134, A302835. Sequence in context: A244738 A215462 A025843 * A178580 A035437 A156996 Adjacent sequences:  A303903 A303904 A303905 * A303907 A303908 A303909 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 02 2018 STATUS approved

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Last modified May 29 15:44 EDT 2020. Contains 334704 sequences. (Running on oeis4.)