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 A332304 Number of compositions (ordered partitions) of n into distinct parts such that number of parts is odd. 14
 0, 1, 1, 1, 1, 1, 7, 7, 13, 19, 25, 31, 43, 49, 61, 193, 205, 337, 475, 727, 985, 1363, 1741, 2359, 2983, 3841, 4705, 5929, 12193, 13777, 20527, 27631, 39901, 52651, 75601, 99151, 132907, 172297, 227053, 287569, 373525, 465241, 587563, 725839, 899761, 1457683 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..5000 FORMULA G.f.: Sum_{k>=1} (2*k - 1)! * x^(k*(2*k - 1)) / Product_{j=1..2*k-1} (1 - x^j). a(n) = A032020(n) - A332305(n). EXAMPLE a(6) = 7 because we have [6], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3]. MAPLE b:= proc(n, i, p) option remember; `if`(i*(i+1)/2 b(n\$2, 0): seq(a(n), n=0..55); # Alois P. Heinz, Feb 09 2020 MATHEMATICA nmax = 45; CoefficientList[Series[Sum[(2 k - 1)! x^(k (2 k - 1))/Product[1 - x^j, {j, 1, 2 k - 1}], {k, 1, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A027193, A032020, A067659, A166444, A332305. Sequence in context: A335895 A072821 A038589 * A317790 A109539 A109541 Adjacent sequences: A332301 A332302 A332303 * A332305 A332306 A332307 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 09 2020 STATUS approved

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Last modified February 3 10:55 EST 2023. Contains 360034 sequences. (Running on oeis4.)