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%I M4686 N2002 #27 Oct 17 2023 08:18:51
%S 1,10,25,37,42,48,79,145,244,415,672,1100,1722,2727,4193,6428,9658,
%T 14478,21313,31304,45329,65311,93074,132026,185413,259242,359395,
%U 495839,679175,926064,1254360,1691753,2268267,3028345,4021954,5320139,7003154
%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 Vincenzo Librandi, <a href="/A002600/b002600.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(6, t)), x, 1+max(6, t)), x, max(6, 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[6, t]], {x, 0, Max[6, t]}]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Mar 13 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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