OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = 2/5 * binomial(n + 1, 4)*(8 - 7*n + 2*n^2).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: -((2 x (x^2 + 5 x^3 + 6 x^4))/(-1 + x)^7).
MATHEMATICA
Table[2/5 Binomial[n + 1, 4] (8 - 7 n + 2 n^2), {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 2, 24, 138, 532, 1596}, 20]
CoefficientList[Series[-((2 (x^2 + 5 x^3 + 6 x^4))/(-1 + x)^7), {x, 0, 20}], x]
PROG
(PARI) a(n)=n*(2*n^5 - 11*n^4 + 20*n^3 - 5*n^2 - 22*n + 16)/60 \\ Charles R Greathouse IV, Aug 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 10 2017
STATUS
approved