OFFSET
0,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: (x^2-x+1)*(x^2-3*x+3)/(x-1)^6.
a(n) = (n+1)*(n^4 +14*n^3 +91*n^2 +254*n +360)/120.
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) for n>6. - Wesley Ivan Hurt, Jan 27 2016
E.g.f.: (360 + 1080*x + 780*x^2 + 220*x^3 + 25*x^4 + x^5)*exp(x)/120. - G. C. Greubel, Nov 24 2017
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3, 12, 34, 80, 166, 314}, 50] (* Vincenzo Librandi, May 12 2015 *)
PROG
(Magma) [(n+1)*(n^4+14*n^3+91*n^2+254*n+360)/120: n in [0..40]]; // Vincenzo Librandi, May 12 2015
(PARI) Vec((x^2-x+1)*(x^2-3*x+3)/(x-1)^6 + O(x^50)) \\ Michel Marcus, Jan 28 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, May 12 2015
STATUS
approved