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A331980 Number of compositions (ordered partitions) of n into distinct odd parts > 1. 0
1, 0, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 4, 1, 4, 7, 6, 7, 6, 13, 8, 19, 8, 25, 34, 31, 34, 43, 60, 49, 84, 61, 134, 73, 158, 205, 232, 217, 280, 355, 378, 487, 450, 745, 572, 1003, 668, 1381, 1558, 1759, 1678, 2383, 2592, 3001, 3480, 3865, 5162, 4729, 6794, 5953, 9964 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..60.

Index entries for sequences related to compositions

FORMULA

G.f.: Sum_{k>=0} k! * x^(k*(k + 2)) / Product_{j=1..k} (1 - x^(2*j)).

EXAMPLE

a(12) = 4 because we have [9, 3], [7, 5], [5, 7] and [3, 9].

MATHEMATICA

nmax = 60; CoefficientList[Series[Sum[k! x^(k (k + 2))/Product[(1 - x^(2 j)), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

CROSSREFS

Сf. A000931, A027349, A032020, A032021, A032022, A087897.

Sequence in context: A287477 A231473 A216652 * A055684 A300584 A024559

Adjacent sequences:  A331977 A331978 A331979 * A331981 A331982 A331983

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 03 2020

STATUS

approved

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Last modified July 29 06:21 EDT 2021. Contains 346340 sequences. (Running on oeis4.)