OFFSET
4,2
LINKS
Colin Barker, Table of n, a(n) for n = 4..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
Sequence satisfies an 8-degree polynomial approximating A002878.
a(n) = (-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320. - Colin Barker, Nov 25 2014
G.f.: x^4*(x^8-5*x^7+11*x^6-10*x^5-x^4+10*x^3-11*x^2+5*x-1) / (x-1)^9. - Colin Barker, Nov 25 2014
From G. C. Greubel, Jul 01 2019: (Start)
E.g.f.: (1169280 + 443520*x + 80640*x^2 + 6720*x^3 +(-1169280 +725760*x -221760*x^2 +47040*x^3 -6720*x^4 +1008*x^5 -56*x^6 +16*x^7 +x^8)*exp(x) )/8!. (End)
MATHEMATICA
Table[(-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320, {n, 4, 40}] (* G. C. Greubel, Jul 01 2019 *)
PROG
(PARI) Vec(x^4*(x^8-5*x^7+11*x^6-10*x^5-x^4+10*x^3-11*x^2+5*x-1)/(x-1)^9 + O(x^40)) \\ Colin Barker, Nov 25 2014
(PARI) for(n=4, 40, print1((-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320, ", ")) \\ G. C. Greubel, Jul 01 2019
(Magma) [(-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320: n in [4..40]]; // G. C. Greubel, Jul 01 2019
(Sage) [(-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320 for n in (4..40)] # G. C. Greubel, Jul 01 2019
(GAP) List([4..40], n-> (-1169280 +1119312*n -517700*n^2 +148092*n^3 -26551*n^4 +2688*n^5 -70*n^6 -12*n^7 +n^8)/40320) # G. C. Greubel, Jul 01 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved