OFFSET
0,3
LINKS
Q. T. Bach, R. Paudyal, J. B. Remmel, A Fibonacci analogue of Stirling numbers, arXiv preprint arXiv:1510.04310 [math.CO], 2015-2016.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 3*C(n+2,4) - C(n,2). - Zerinvary Lajos, May 02 2007, corrected Jun 12 2018
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) = n*(n-1)*(n^2+3*n-2)/8. [R. J. Mathar, Oct 30 2009]
G.f.: x^2*(-2-2*x+x^2)/(x-1)^5. [R. J. Mathar, Oct 30 2009]
EXAMPLE
a(3) = t(t(3))-3^2 = t(6)-9 = 21-9 = 12.
MAPLE
seq(3*binomial(n+2, 4)-binomial(n, 2), n=0..35); # Zerinvary Lajos, May 02 2007
MATHEMATICA
Table[n (n - 1) (n^2 + 3 n - 2)/8, {n, 0, 40}] (* Bruno Berselli, Aug 27 2014 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 2, 12, 39}, 60] (* Harvey P. Dale, Apr 04 2023 *)
PROG
(PARI) t(i)=i*(i+1)/2
vector(40, i, t(t(i))-i^2)
(Magma) [n*(n-1)*(n^2+3*n-2)/8: n in [0..40]]; // Vincenzo Librandi, Jun 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Jul 23 2003
STATUS
approved