%I M4965 N2130 #23 Oct 17 2023 08:19:00

%S 1,15,51,97,127,145,152,160,273,481,811,1372,2250,3692,5924,9472,

%T 14887,23310,36005,55314,84042,126998,190138,283108,418175,614429,

%U 896439,1301168,1876826,2693988,3845134,5462744,7720947,10864828,15216527

%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="/A002602/b002602.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(8, t)), x, 1+max(8, t)), x, max(8, 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[8, t]], {x, 0, Max[8, t]}]; Table[ a[n], {n, 1, 40}] (* _Jean-François 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