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 A305551 Number of partitions of partitions of n where all partitions have the same sum. 42
 1, 1, 3, 4, 9, 8, 22, 16, 43, 41, 77, 57, 201, 102, 264, 282, 564, 298, 1175, 491, 1878, 1509, 2611, 1256, 7872, 2421, 7602, 8026, 16304, 4566, 38434, 6843, 48308, 41078, 56582, 28228, 221115, 21638, 146331, 208142, 453017, 44584, 844773, 63262, 1034193, 1296708 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{d|n} binomial(A000041(n/d) + d - 1, d). EXAMPLE The a(4) = 9 partitions of partitions where all partitions have the same sum: (4), (31), (22), (211), (1111), (2)(2), (2)(11), (11)(11), (1)(1)(1)(1). MATHEMATICA Table[Sum[Binomial[PartitionsP[n/k]+k-1, k], {k, Divisors[n]}], {n, 60}] PROG (PARI) a(n)={if(n<1, n==0, sumdiv(n, d, binomial(numbpart(n/d) + d - 1, d)))} \\ Andrew Howroyd, Jun 22 2018 CROSSREFS Cf. A000005, A001970, A001315, A007716, A038041, A055887, A063834, A271619, A289078, A298422, A306017. Sequence in context: A280616 A317099 A317715 * A306018 A076120 A082188 Adjacent sequences: A305548 A305549 A305550 * A305552 A305553 A305554 KEYWORD nonn AUTHOR Gus Wiseman, Jun 20 2018 STATUS approved

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Last modified June 2 13:38 EDT 2023. Contains 363097 sequences. (Running on oeis4.)