A071953 Diagonal T(n,n-2) of triangle in A071951.
4, 52, 292, 1092, 3192, 7896, 17304, 34584, 64284, 112684, 188188, 301756, 467376, 702576, 1028976, 1472880, 2065908, 2845668, 3856468, 5150068, 6786472, 8834760, 11373960, 14493960, 18296460, 22895964, 28420812, 35014252
Offset: 3
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 3..5000
- W. N. Everitt, L. L. Littlejohn and R. Wellman, Legendre polynomials, Legendre-Stirling numbers and the left-definite spectral analysis of the Legendre differential expression, J. Comput. Appl. Math. 148, 2002, 213-238.
- L. L. Littlejohn and R. Wellman, A general left-definite theory for certain self-adjoint operators with applications to differential equations, J. Differential Equations, 181(2), 2002, 280-339.
- Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
Programs
-
GAP
List([3..30], n-> (n-2)*(n-1)*n*(n+1)*(5*n^2 - 11*n + 3)/90); # G. C. Greubel, Mar 16 2019
-
Magma
[(n-2)*(n-1)*n*(n+1)*(5*n^2 - 11*n + 3)/90: n in [3..30]]; // G. C. Greubel, Mar 16 2019
-
Mathematica
Flatten[ Table[ Sum[(-1)^{r + n - 2}(2r + 1)(r^2 + r)^n/((r + n - 1)!(n - 2 - r)!), {r, 1, n - 2}], {n, 3, 34}]] Table[(n-2)(n-1)n(n+1)(5n^2-11n+3)/90,{n,3,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{4,52,292,1092,3192, 7896,17304}, 30] (* Harvey P. Dale, Jul 03 2011 *) -
PARI
{a(n) = (n-2)*(n-1)*n*(n+1)*(5*n^2 - 11*n + 3)/90}; \\ G. C. Greubel, Mar 16 2019 -
Sage
[(n-2)*(n-1)*n*(n+1)*(5*n^2 - 11*n + 3)/90 for n in (3..30)] # G. C. Greubel, Mar 16 2019
Formula
a(n) = (n-2)*(n-1)*n*(n+1)*(5*n^2 - 11*n + 3)/90.
a(0)=4, a(1)=52, a(2)=292, a(3)=1092, a(4)=3192, a(5)=7896, a(6)=17304, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Jul 03 2011
G.f.: 4*(3*x*(x+2)+1)/(1-x)^7. - Harvey P. Dale, Jul 03 2011
E.g.f.: x^3*(60 + 135*x + 54*x^2 + 5*x^3)*exp(x)/90. - G. C. Greubel, Mar 16 2019
Extensions
More terms from Robert G. Wilson v, Jun 19 2002