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 A332305 Number of compositions (ordered partitions) of n into distinct parts such that number of parts is even. 11
 1, 0, 0, 2, 2, 4, 4, 6, 6, 8, 32, 34, 58, 84, 132, 158, 230, 280, 376, 450, 570, 1388, 1556, 2398, 3310, 4920, 6600, 9674, 12122, 16684, 21340, 28110, 34974, 45392, 55208, 69274, 124498, 143676, 204012, 270758, 377966, 493024, 690304, 895434, 1223826, 1562948 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..5000 FORMULA G.f.: Sum_{k>=0} (2*k)! * x^(k*(2*k + 1)) / Product_{j=1..2*k} (1 - x^j). a(n) = A032020(n) - A332304(n). EXAMPLE a(5) = 4 because we have [4, 1], [3, 2], [2, 3] and [1, 4]. 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)! x^(k (2 k + 1))/Product[1 - x^j, {j, 1, 2 k}], {k, 0, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A027187, A032020, A034008, A067661, A332304. Sequence in context: A259881 A238132 A278296 * A340282 A008642 A001364 Adjacent sequences:  A332302 A332303 A332304 * A332306 A332307 A332308 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 09 2020 STATUS approved

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Last modified May 19 13:24 EDT 2022. Contains 353833 sequences. (Running on oeis4.)