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A339169
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Number of compositions (ordered partitions) of n into distinct parts, the least being 6.
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3
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0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 56, 62, 86, 116, 140, 170, 218, 248, 296, 350, 518, 572, 764, 938, 1250, 1448, 1880, 2198, 2774, 3212, 3908, 5210, 6146, 7568, 9368, 11750, 14510, 17756, 21476, 26402, 31826, 38432, 45536
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OFFSET
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0,14
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} k! * x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j).
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EXAMPLE
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a(21) = 8 because we have [15, 6], [8, 7, 6], [8, 6, 7], [7, 8, 6], [7, 6, 8], [6, 15], [6, 8, 7] and [6, 7, 8].
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MATHEMATICA
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nmax = 62; CoefficientList[Series[Sum[k! x^(k (k + 11)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A026799, A026827, A339104, A339162, A339163, A339164, A339165, A339166, A339170, A339171, A339172.
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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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