OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Wolfdieter Lang, On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles, arXiv:1708.01421 [math.NT], August 2017.
FORMULA
a(n) = n*(n+1)*(n+2)*(n+3)*(15*n^4+150*n^3+515*n^2+672*n+223)/360.
G.f.: -x*(x^4+112*x^3+718*x^2+744*x+105) / (x-1)^9. - Colin Barker, Aug 15 2014
a(n) = A000332(n+3) * (15*n^4+150*n^3+515*n^2+672*n+223)/15 . - R. J. Mathar, Oct 01 2016
a(n) = A(n+4, n-1), n >= 1 (fifth diagonal). See a crossref. below. - Wolfdieter Lang, Jul 21 2017
MATHEMATICA
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {105, 1689, 12139, 57379, 208054, 626934, 1646778, 3889578, 8439783}, 30] (* Harvey P. Dale, May 28 2018 *)
PROG
(PARI) Vec(-x*(x^4+112*x^3+718*x^2+744*x+105)/(x-1)^9 + O(x^100)) \\ Colin Barker, Aug 15 2014
CROSSREFS
From Johannes W. Meijer, Jun 08 2009: (Start)
Equals fifth right hand column of A028338 triangle.
Equals fifth left hand column of A109692 triangle.
Equals fifth right hand column of A161198 triangle divided by 2^m.
(End)
KEYWORD
nonn,easy
AUTHOR
STATUS
approved