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A321508
Expansion of Product_{k>=1} 1/(1 - x^prime(k))^A056768(k).
0
1, 0, 1, 1, 1, 3, 2, 6, 4, 7, 10, 15, 17, 30, 31, 41, 58, 81, 105, 143, 177, 218, 306, 393, 550, 618, 883, 1024, 1395, 1810, 2372, 2985, 3682, 4762, 6077, 7634, 10160, 12517, 15448, 19820, 24754, 32108, 40085, 50851, 62331, 78548, 98505, 125596, 156565
OFFSET
0,6
COMMENTS
a(n) is the number of partitions of n into prime parts prime(k) of A056768(k) kinds.
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^A000040(k))^A000607(A000040(k)).
EXAMPLE
a(7) = 6 because we have [{7}], [{5, 2}], [{5}, {2}], [{3, 2, 2}], [{3, 2}, {2}] and [{3}, {2}, {2}].
MATHEMATICA
b[n_] := b[n] = SeriesCoefficient[Product[1/(1 - x^Prime[k]), {k, 1, n}], {x, 0, Prime[n]}]; a[n_] := a[n] = SeriesCoefficient[Product[1/(1 - x^Prime[k])^b[k], {k, 1, n}], {x, 0, n}]; Table[a[n], {n, 0, 48}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 11 2018
STATUS
approved