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A290792
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Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)^2*(k+2)/12)).
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3
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1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 18, 18, 19, 19, 20, 20, 22, 22, 23, 23, 25, 25, 27, 27, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 45, 45, 47, 47, 49, 49, 52, 52, 54, 54, 57
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OFFSET
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0,7
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COMMENTS
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Number of partitions of n into nonzero 4-dimensional pyramidal numbers (A002415).
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)^2*(k+2)/12)).
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EXAMPLE
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a(12) = 3 because we have [6, 6], [6, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
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MAPLE
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N:= 100: # for a(0)..a(N)
P:= 1:
for k from 1 do
e:= k*(k+1)^2*(k+2)/12;
if e > N then break fi;
P:= P/(1-x^e);
od:
S:= series(P, x, N+1):
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MATHEMATICA
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nmax = 90; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)^2 (k + 2)/12)), {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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