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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 16 2002
EXTENSIONS
More terms from Robert G. Wilson v, Jun 19 2002
STATUS
approved