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 A304329 Expansion of Product_{k>0} (Sum_{m>=0} x^(k*m^3)). 3
 1, 1, 1, 2, 2, 3, 4, 5, 7, 8, 11, 13, 16, 20, 24, 30, 36, 44, 51, 62, 74, 88, 103, 122, 145, 169, 197, 231, 268, 312, 362, 419, 485, 557, 642, 737, 846, 967, 1108, 1262, 1442, 1640, 1865, 2118, 2398, 2719, 3074, 3474, 3922, 4421, 4980, 5604, 6294, 7070, 7929 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also the number of partitions of n in which each part occurs a cube number (>=0) of times. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Seiichi Manyama) EXAMPLE n | Partitions of n in which each part occurs a cube number (>=0) of times --+----------------------------------------------------------------------- 1 | 1; 2 | 2; 3 | 3 = 2+1; 4 | 4 = 3+1; 5 | 5 = 4+1 = 3+2; 6 | 6 = 5+1 = 4+2 = 3+2+1; 7 | 7 = 6+1 = 5+2 = 4+3 = 4+2+1; 8 | 8 = 7+1 = 6+2 = 5+3 = 5+2+1 = 4+3+1 = 1+1+1+1+1+1+1+1; MAPLE b:= proc(n, i) option remember; local j; if n=0 then 1       elif i<1 then 0 else b(n, i-1); for j while         i*j^3<=n do %+b(n-i*j^3, i-1) od; % fi     end: a:= n-> b(n\$2): seq(a(n), n=0..60);  # Alois P. Heinz, May 11 2018 MATHEMATICA terms = 100; Product[Sum[x^(k*m^3), {m, 0, Ceiling[terms^(1/3)]}], {k, 1, terms}] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Mar 08 2021 *) CROSSREFS Cf. A000041, A300446. Sequence in context: A095699 A112192 A017841 * A111901 A316202 A326671 Adjacent sequences:  A304326 A304327 A304328 * A304330 A304331 A304332 KEYWORD nonn AUTHOR Seiichi Manyama, May 11 2018 STATUS approved

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Last modified April 22 18:24 EDT 2021. Contains 343177 sequences. (Running on oeis4.)