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A002598 A generalized partition function.
(Formerly M4077 N1693)
2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Oct 13 2013
STATUS
approved

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Last modified April 23 10:29 EDT 2024. Contains 371905 sequences. (Running on oeis4.)