A107942 a(n) = (n+1)(n+2)^3*(n+3)^3*(n+4)(2n+5)/4320.
1, 28, 300, 1925, 8918, 32928, 102816, 282150, 698775, 1591876, 3383380, 6782139, 12931100, 23609600, 41505024, 70570332, 116486397, 187250700, 293916700, 451511137, 680159634, 1006454240, 1465100000, 2100881250, 2970992115
Offset: 0
Links
- Antoine Bourget, Amihay Hanany, Dominik Miketa, Quiver origami: discrete gauging and folding, arXiv:2005.05273 [hep-th], 2020. See Eq. (3.50), 1st row in Fig. 8, and top box in Fig. 9.
- S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).
- J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=0]
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Maple
a:=n->(1/4320)*(n+1)*(n+2)^3*(n+3)^3*(n+4)*(2*n+5): seq(a(n),n=0..30);
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Mathematica
Table[(1/4320)(n+1)(n+2)^3(n+3)^3(n+4)(2n+5),{n,0,30}] (* Harvey P. Dale, Nov 03 2011 *)
Formula
G.f.: (x+1)*(x^4+17*x^3+48*x^2+17*x+1)/(x-1)^10. - Colin Barker, Sep 20 2012
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Wesley Ivan Hurt, Jun 23 2020
Comments