OFFSET
0,1
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
A. van Heemert, Cyclic permutations with sequences and related problems, J. Reine Angew. Math., 198 (1957), 56-72.
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
FORMULA
For n>=0 a(n) = n!*(n^4 + 6*n^3 + 17*n^2 + 20*n + 9). - Benoit Cloitre, Jun 10 2004
G.f.: -log(-x+1)+1+2/(x-1)^4*x*(4-3*x+2*x^2). - Simon Plouffe, Master's Thesis, Uqam 1992
E.g.f.: (9 + 8*x + 6*x^2 + x^4)/(1 - x)^5. - Ilya Gutkovskiy, Jan 20 2017
a(n) = (n+5)*a(n-1) - (n-1)*a(n-2) with a(0) = 9 and a(1) = 53. Cf. A095177. - Peter Bala, Jul 22 2021
MATHEMATICA
Table[(n^4 + 6*n^3 + 17*n^2 + 20*n + 9) n!, {n, 0, 20}] (* T. D. Noe, Aug 09 2012 *)
Differences[Range[0, 30]!, 4] (* Harvey P. Dale, Jun 06 2017 *)
PROG
(PARI) a(n)=if(n<0, 0, n!*(n^4 + 6*n^3 + 17*n^2 + 20*n + 9))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved