A002600 A generalized partition function. (Formerly M4686 N2002)

1, 10, 25, 37, 42, 48, 79, 145, 244, 415, 672, 1100, 1722, 2727, 4193, 6428, 9658, 14478, 21313, 31304, 45329, 65311, 93074, 132026, 185413, 259242, 359395, 495839, 679175, 926064, 1254360, 1691753, 2268267, 3028345, 4021954, 5320139, 7003154

Offset

1,2

References

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

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

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Hansraj Gupta, A generalization of the partition function, Proc. Nat. Inst. Sci. India 17 (1951), 231-238. [Annotated scanned copy]

Maple

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

Mathematica

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 *)

Crossrefs

Sequence in context: A345651 A154057 A074814 * A087473 A014120 A003001

Adjacent sequences: A002597 A002598 A002599 * A002601 A002602 A002603

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Jul 20 2009

Status

approved