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A generalized partition function.
(Formerly M4106 N1703)
1

%I M4106 N1703 #28 Oct 17 2023 07:41:20

%S 1,6,15,19,24,42,73,127,208,337,528,827,1263,1902,2819,4133,5986,8578,

%T 12146,17057,23711,32708,44726,60713,81800,109468,145526,192288,

%U 252521,329792,428316,553478,711596,910563,1159790,1470798,1857286,2335838

%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="/A002599/b002599.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(5, t)), x, 1+max(5, t)), x, max(5, 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[5, t]], {x, 0, Max[5, 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