OFFSET
0,6
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.5.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = (n-4)*(n-3)*(n-2)*(n-1)*n*(n^5 + 5*n^4 + 5*n^3 - 85*n^2 - 374*n - 960)/3840.
G.f.: x^5*(60+1041*x-459*x^2+411*x^3-129*x^4+21*x^5)/(1-x)^11. - Colin Barker, May 08 2012
E.g.f.: x^5*(1920 + 7152*x + 3280*x^2 + 560*x^3 + 40*x^4 + x^5)*exp(x)/3840. - G. C. Greubel, May 15 2019
MATHEMATICA
Table[Binomial[n, 5]*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32, {n, 0, 30}] (* G. C. Greubel, May 15 2019 *)
PROG
(PARI) {a(n) = binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32}; \\ G. C. Greubel, May 15 2019
(Magma) [Binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32: n in [0..30]]; // G. C. Greubel, May 15 2019
(Sage) [binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32 for n in (0..30)] # G. C. Greubel, May 15 2019
(GAP) List([0..30], n-> Binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32) # G. C. Greubel, May 15 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 16 2000
STATUS
approved