OFFSET
1,4
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = binomial(n + 1, 4)*(-62 + 11*n - 109*n^2 + 40*n^3)/70.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
G.f.: (x (x^2 + 49 x^3 + 58 x^4 + 12 x^5))/(-1 + x)^8.
MATHEMATICA
Table[Binomial[n + 1, 4] (-62 + 11 n - 109 n^2 + 40 n^3)/70, {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 1, 57, 486, 2360, 8394, 24354}, 40]
CoefficientList[Series[(x^2 + 49 x^3 + 58 x^4 + 12 x^5)/(-1 + x)^8, {x, 0, 20}], x]
PROG
(PARI) a(n)=n*(40*n^6 - 189*n^5 + 189*n^4 + 105*n^3 - 105*n^2 + 84*n - 124)/1680 \\ Charles R Greathouse IV, Aug 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 10 2017
STATUS
approved