A027970 a(n) = T(n, 2*n-8), T given by A027960.

1, 4, 11, 29, 76, 196, 487, 1148, 2552, 5353, 10636, 20120, 36425, 63415, 106630, 173821, 275603, 426242, 644593, 955207, 1389626, 1987886, 2800249, 3889186, 5331634, 7221551, 9672794, 12822346, 16833919, 21901961, 28256096

Offset: 4

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

A column of triangle A026998.

Programs

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

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

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 *)

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

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

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)

a(n) = A027971(n+1) - A027971(n).

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)