OFFSET
4,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 4..1004
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
E. G. Whitehead, Jr., Stirling number identities from chromatic polynomials, J. Combin. Theory, A 24 (1978), 314-317.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = n^4 - 16*n^3 + 102*n^2 - 300*n + 340.
G.f.: x^4*(4-5*x+17*x^2+x^3+7*x^4)/(1-x)^5. - Harvey P. Dale, Dec 25 2012
E.g.f.: (1/6)*(-2040 - 762*x - 108*x^2 - 7*x^3 + (2040 - 1278*x + 366*x^2 - 60*x^3 + 6*x^4)*exp(x)). - G. C. Greubel, Dec 01 2022
MAPLE
A005492:=-(15-23*z+41*z**2-13*z**3+4*z**4)/(z-1)**5; # Conjectured by Simon Plouffe in his 1992 dissertation. Gives sequence except for the leading 4.
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {4, 15, 52, 151, 372}, 50] (* Harvey P. Dale, Dec 25 2012 *)
PROG
(Magma) [n^4 -16*n^3 +102*n^2 -300*n +340: n in [4..50]]; // G. C. Greubel, Dec 01 2022
(SageMath) [n^4 -16*n^3 +102*n^2 -300*n +340 for n in range(4, 51)] # G. C. Greubel, Dec 01 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004
STATUS
approved