OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Wolfdieter Lang, On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles, arXiv:1708.01421 [math.NT], August 2017.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n*(n+1)*(9*n^2+9*n-2)/8.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Clark Kimberling, Aug 18 2012
G.f.: (4 + 19*x + 4*x^2)/(1 - x)^5. - Clark Kimberling, Aug 18 2012
From Wolfdieter Lang, Jul 30 2017: (Start)
E.g.f.: exp(x)*x*(32+124*x+72*x^2+9*x^3)/8 = exp(x)*x*(2 + x)*(16 + 54*x + 9*x^2)/8.
a(n) = A286718(n+1, n-1), n >= 1. (End)
MATHEMATICA
Table[n(n+1)(9n^2+9n-2)/8, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {4, 39, 159, 445, 1005}, 40] (* Harvey P. Dale, Oct 16 2023 *)
PROG
(Magma) [n*(n+1)*(9*n^2+9*n-2)/8: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved