A002598 A generalized partition function. (Formerly M4077 N1693)

1, 6, 9, 13, 19, 37, 58, 97, 143, 227, 328, 492, 688, 992, 1364, 1903, 2551, 3473, 4586, 6097, 7911, 10333, 13226, 16988, 21454, 27172, 33938, 42437, 52423, 64833, 79354, 97130, 117824, 142930, 172018, 206925, 247179, 295105, 350154, 415124, 489414, 576540

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]

Index entries for linear recurrences with constant coefficients, signature (1, 2, 1, 0, -9, -5, 2, 13, 21, -4, -17, -30, -13, 25, 28, 25, -13, -30, -17, -4, 21, 13, 2, -5, -9, 0, 1, 2, 1, -1).

Formula

G.f.: x*(3*x^32 -9*x^30 -10*x^29 -2*x^28 +29*x^27 +43*x^26 +9*x^25 -54*x^24 -107*x^23 -49*x^22 +76*x^21 +162*x^20 +125*x^19 -53*x^18 -189*x^17 -172*x^16 -11*x^15 +157*x^14 +166*x^13 +50*x^12 -81*x^11 -119*x^10 -49*x^9 +30*x^8 +55*x^7 +29*x^6 -8*x^5 -18*x^4 -9*x^3 +x^2 +5*x +1)/((x -1)^10*(x +1)^6*(x^2 +1)^4*(x^2 +x +1)^3). [Colin Barker, Oct 02 2012]

Mathematica

CoefficientList[Series[(3 x^32 - 9 x^30 - 10 x^29 - 2 x^28 + 29 x^27 + 43 x^26 + 9 x^25 - 54 x^24 - 107 x^23 - 49 x^22 + 76 x^21 + 162 x^20 + 125 x^19 - 53 x^18 - 189 x^17 - 172 x^16 - 11 x^15 + 157 x^14 + 166 x^13 + 50 x^12 - 81 x^11 - 119 x^10 - 49 x^9 + 30 x^8 + 55 x^7 + 29 x^6 - 8 x^5 - 18 x^4 - 9 x^3 + x^2 + 5 x + 1)/((x - 1)^10 (x + 1)^6 (x^2 + 1)^4 (x^2 + x + 1)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 13 2013 *)

Crossrefs

Essentially the same as A064349.

Sequence in context: A315969 A092949 A048626 * A315970 A315971 A315972

Adjacent sequences: A002595 A002596 A002597 * A002599 A002600 A002601

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Oct 13 2013

Status

approved