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A329384
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G.f.: (1 + x) * (1 + x^2) * (1 + x^3) * Product_{k>=1} (1 + x^k).
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1
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1, 2, 3, 6, 8, 11, 16, 20, 26, 34, 43, 54, 68, 84, 103, 127, 154, 186, 225, 269, 321, 383, 453, 535, 631, 740, 866, 1012, 1178, 1368, 1587, 1835, 2117, 2440, 2804, 3217, 3687, 4215, 4812, 5487, 6244, 7096, 8055, 9128, 10331, 11681, 13187, 14870, 16752, 18846, 21180
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OFFSET
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0,2
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COMMENTS
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Number of partitions of n into distinct parts if there are two types of 1's, two types of 2's and two types of 3's.
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LINKS
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FORMULA
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MATHEMATICA
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nmax = 50; CoefficientList[Series[(1 + x) (1 + x^2) (1 + x^3) Product[(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Sum[(-1)^(k/d + 1) If[d < 4, 2, 1] d, {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 50}]
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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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