OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Binomial Transform
Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).
FORMULA
O.g.f.: x*(1 - 2*x + 6*x^2 - 8*x^3 + 4*x^4)/(1 - 2*x)^4.
E.g.f.: x*(1 + exp(2*x)*(3 + 6*x + 2*x^2))/4.
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 5.
a(n) = 2^(n-4)*n*(n + 1)*(n + 2) with a(0) = 0 and a(1) = 1.
a(n) ~ A128789(n)/16.
Sum_{n>0} 1/a(n) = 8*log(2) - 13/3 = 1.21184411114622914200452363833...
MATHEMATICA
LinearRecurrence[{8, -24, 32, -16}, {0, 1, 6, 30, 120, 420}, 30]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Jul 08 2021
STATUS
approved