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 A300301 Number of ways to choose a partition, with odd parts, of each part of a partition of n into odd parts. 11
 1, 1, 1, 3, 3, 6, 10, 15, 21, 37, 56, 80, 127, 183, 280, 428, 616, 893, 1367, 1944, 2846, 4223, 6049, 8691, 12670, 18128, 25921, 37529, 53338, 75738, 108561, 153460, 216762, 308829, 433893, 612006, 864990, 1211097, 1697020, 2386016, 3331037, 4648229, 6503314 (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 O.g.f.: Product_{n odd} 1/(1 - A000009(n)x^n). EXAMPLE The a(6) = 10 twice-partitions using odd partitions: (5)(1), (3)(3), (113)(1), (3)(111), (111)(3), (3)(1)(1)(1), (11111)(1), (111)(111), (111)(1)(1)(1), (1)(1)(1)(1)(1)(1). MAPLE with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add(      `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)     end: g:= proc(n, i) option remember; `if`(n=0 or i=1, 1,       g(n, i-2)+`if`(i>n, 0, b(i)*g(n-i, i)))     end: a:= n-> g(n, n-1+irem(n, 2)): seq(a(n), n=0..50);  # Alois P. Heinz, Mar 05 2018 MATHEMATICA nn=50; ser=Product[1/(1-PartitionsQ[n]x^n), {n, 1, nn, 2}]; Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}] CROSSREFS A300300(n) <= a(n) <= A279785(n) Cf. A000009, A063834, A078408, A089259, A270995, A271619, A279374, A279375, A279790, A294617, A300300. Sequence in context: A226642 A266137 A265506 * A031504 A298164 A304265 Adjacent sequences:  A300298 A300299 A300300 * A300302 A300303 A300304 KEYWORD nonn AUTHOR Gus Wiseman, Mar 02 2018 STATUS approved

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Last modified January 19 21:38 EST 2022. Contains 350466 sequences. (Running on oeis4.)