A339169 - OEIS

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A339169

Number of compositions (ordered partitions) of n into distinct parts, the least being 6.

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

0,14

LINKS

Table of n, a(n) for n=0..62.

Index entries for sequences related to compositions

FORMULA

G.f.: Sum_{k>=1} k! * x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j).

EXAMPLE

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].

MATHEMATICA

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]