A002599 A generalized partition function. (Formerly M4106 N1703)

1, 6, 15, 19, 24, 42, 73, 127, 208, 337, 528, 827, 1263, 1902, 2819, 4133, 5986, 8578, 12146, 17057, 23711, 32708, 44726, 60713, 81800, 109468, 145526, 192288, 252521, 329792, 428316, 553478, 711596, 910563, 1159790, 1470798, 1857286, 2335838

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(5, t)), x, 1+max(5, t)), x, max(5, 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[5, t]], {x, 0, Max[5, t]}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 13 2014, after Alois P. Heinz *)

Crossrefs

Sequence in context: A362141 A044058 A105139 * A001484 A217480 A335417

Adjacent sequences: A002596 A002597 A002598 * A002600 A002601 A002602

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Jul 20 2009

Status

approved