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A002601 A generalized partition function.
(Formerly M4694 N2004)

%I M4694 N2004 #26 Oct 17 2023 08:18:55

%S 1,10,34,58,73,79,86,152,265,457,763,1268,2058,3308,5236,8220,12731,

%T 19546,29685,44702,66714,98806,145154,211756,306667,441249,630771,

%U 896344,1266146,1778692,2485086,3454206,4777165,6575350,9008159

%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="/A002601/b002601.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(7, t)), x, 1+max(7, t)), x, max(7, 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[7, t]], {x, 0, Max[7, 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 April 24 05:19 EDT 2024. Contains 371918 sequences. (Running on oeis4.)