A002602 - OEIS

A002602

A generalized partition function.
(Formerly M4965 N2130)

1, 15, 51, 97, 127, 145, 152, 160, 273, 481, 811, 1372, 2250, 3692, 5924, 9472, 14887, 23310, 36005, 55314, 84042, 126998, 190138, 283108, 418175, 614429, 896439, 1301168, 1876826, 2693988, 3845134, 5462744, 7720947, 10864828, 15216527

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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(8, t)), x, 1+max(8, t)), x, max(8, 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[8, t]], {x, 0, Max[8, t]}]; Table[ a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A044117 A044498 A138082 * A098831 A265039 A039405

Adjacent sequences: A002599 A002600 A002601 * A002603 A002604 A002605

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Alois P. Heinz, Jul 20 2009

STATUS

approved