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 A071953 Diagonal T(n,n-2) of triangle in A071951. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 REFERENCES 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. LINKS FORMULA (n-2)(n-1)n(n+1)(5n^2-11n+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) [From Harvey P. Dale, July 03 2011] G.f.: -((4*(3*x*(x+2)+1))/(x-1)^7) [From Harvey P. Dale, July 03 2011] 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] (* From Harvey P. Dale, July 03 2011 *) CROSSREFS Sequence in context: A000854 A110908 A101354 * A221727 A144339 A155661 Adjacent sequences:  A071950 A071951 A071952 * A071954 A071955 A071956 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 16 2002 EXTENSIONS More terms from Robert G. Wilson v, Jun 19 2002 STATUS approved

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