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A005492
From expansion of falling factorials.
(Formerly M3495)
2
4, 15, 52, 151, 372, 799, 1540, 2727, 4516, 7087, 10644, 15415, 21652, 29631, 39652, 52039, 67140, 85327, 106996, 132567, 162484, 197215, 237252, 283111, 335332, 394479, 461140, 535927, 619476, 712447, 815524, 929415, 1054852, 1192591, 1343412, 1508119, 1687540
OFFSET
4,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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.
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
Row n=4 of A108087 (shifted and first term prepended).
Cf. A005490.
Sequence in context: A303843 A107307 A240365 * A003013 A117202 A291011
KEYWORD
nonn,easy
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004
STATUS
approved