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

3,1

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).

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

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 *)

Prog

(PARI) {a(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
(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
(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

Crossrefs

Cf. A071951, A071952.

Sequence in context: A297764 A101354 A229146 * A247746 A221727 A144339

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