A005492 From expansion of falling factorials. (Formerly M3495)

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

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

Row n=4 of A108087 (shifted and first term prepended).

Cf. A005490.

Sequence in context: A303843 A107307 A240365 * A003013 A117202 A291011

Adjacent sequences: A005489 A005490 A005491 * A005493 A005494 A005495

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004

Status

approved