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A002603 A generalized partition function.
(Formerly M4971 N2134)

%I M4971 N2134 #21 Oct 17 2023 08:19:05

%S 1,15,73,143,208,244,265,273,282,490,838,1426,2367,3908,6356,10246,

%T 16327,25812,40379,62748,96660,147833,224446,338584,507293,755612,

%U 1118679,1647023,2411642,3513096,5091511,7344086,10543419,15068833,21442703,30385111,42880601

%N A generalized partition function.

%D Hansraj Gupta, A generalization of the partition function. Proc. Nat. Inst. Sci. India 17 (1951), 231-238.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A002603/b002603.txt">Table of n, a(n) for n = 1..1000</a>

%H Hansraj Gupta, <a href="/A002597/a002597.pdf">A generalization of the partition function</a>, Proc. Nat. Inst. Sci. India 17 (1951), 231-238. [Annotated scanned copy]

%p 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

%t 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-Fran├žois Alcover_, Mar 17 2014, after _Alois P. Heinz_ *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Alois P. Heinz_, Jul 20 2009

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)