A002601 A generalized partition function. (Formerly M4694 N2004)

1, 10, 34, 58, 73, 79, 86, 152, 265, 457, 763, 1268, 2058, 3308, 5236, 8220, 12731, 19546, 29685, 44702, 66714, 98806, 145154, 211756, 306667, 441249, 630771, 896344, 1266146, 1778692, 2485086, 3454206, 4777165, 6575350, 9008159

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

Alois P. Heinz, 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(7, t)), x, 1+max(7, t)), x, max(7, 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[7, t]], {x, 0, Max[7, t]}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)

Crossrefs

Sequence in context: A195900 A322412 A247129 * A020495 A155486 A225276

Adjacent sequences: A002598 A002599 A002600 * A002602 A002603 A002604

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Jul 20 2009

Status

approved