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A339170 Number of compositions (ordered partitions) of n into distinct parts, the least being 7. 3
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 32, 62, 62, 92, 116, 146, 170, 224, 248, 302, 350, 404, 572, 650, 818, 1016, 1328, 1526, 1958, 2300, 2852, 3314, 4010, 4592, 6248, 6974, 8750, 10436, 13196, 15722, 19442, 22952 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,16

LINKS

Table of n, a(n) for n=0..64.

Index entries for sequences related to compositions

FORMULA

G.f.: Sum_{k>=1} k! * x^(k*(k + 13)/2) / Product_{j=1..k-1} (1 - x^j).

EXAMPLE

a(24) = 8 because we have [17, 7], [9, 8, 7], [9, 7, 8], [8, 9, 7], [8, 7, 9], [7, 17], [7, 9, 8] and [7, 8, 9].

MATHEMATICA

nmax = 64; CoefficientList[Series[Sum[k! x^(k (k + 13)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A026800, A026828, A339108, A339162, A339163, A339164, A339165, A339166, A339169, A339171, A339172.

Sequence in context: A244464 A250201 A252375 * A257773 A164898 A100801

Adjacent sequences:  A339167 A339168 A339169 * A339171 A339172 A339173

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 25 2020

STATUS

approved

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Last modified January 18 05:18 EST 2021. Contains 340250 sequences. (Running on oeis4.)