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A002603
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A generalized partition function.
(Formerly M4971 N2134)
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1
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1, 15, 73, 143, 208, 244, 265, 273, 282, 490, 838, 1426, 2367, 3908, 6356, 10246, 16327, 25812, 40379, 62748, 96660, 147833, 224446, 338584, 507293, 755612, 1118679, 1647023, 2411642, 3513096, 5091511, 7344086, 10543419, 15068833, 21442703, 30385111, 42880601
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OFFSET
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1,2
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REFERENCES
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Hansraj Gupta, A generalization of the partition function. Proc. Nat. Inst. Sci. India 17 (1951), 231-238.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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J:= m-> product((1-x^j)^(-j), j=1..m): a:= t-> coeff(series(J(min(9, t)), x, 1+max(9, t)), x, max(9, t)): seq(a(n), n=1..40); # Alois P. Heinz, Jul 20 2009
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MATHEMATICA
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J[m_] := Product[(1-x^j)^-j, {j, 1, m}]; a[t_] := SeriesCoefficient[J[Min[9, t]], {x, 0, Max[9, t]}]; Table[ a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)
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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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