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A035444
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Number of partitions of n into parts 4k.
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17
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1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 15, 0, 0, 0, 22, 0, 0, 0, 30, 0, 0, 0, 42, 0, 0, 0, 56, 0, 0, 0, 77, 0, 0, 0, 101, 0, 0, 0, 135, 0, 0, 0, 176, 0, 0, 0, 231, 0, 0, 0, 297, 0, 0, 0, 385, 0, 0, 0, 490, 0, 0, 0, 627, 0, 0, 0, 792, 0, 0, 0, 1002, 0
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OFFSET
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0,9
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LINKS
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FORMULA
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G.f.: 1 / Product_{n>=1} 1 - q^(4*n). - Joerg Arndt, Aug 26 2015
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MAPLE
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seq(coeff(series(mul(1/(1-x^(4*k)), k=1..n), x, n+1), x, n), n=0..105); # Muniru A Asiru, Jul 22 2018
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MATHEMATICA
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nmax=100; CoefficientList[Series[Product[1/(1 - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vincenzo Librandi, Jul 04 2018 *)
nmax = 50; kmax = nmax/4; s = Range[0, kmax]*4;
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Aug 03 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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