OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-8).
FORMULA
a(n) = Sum_{k=0..n} A323100(n - k, k).
a(n) = n! [x^n] exp(x)*(exp(x)*(2*x + 1) - sin(x) - cos(x))/2.
a(n) = 2*((2*n+2)*a(n-3) - (3*n+2)*a(n-2) + (2*n+1)*a(n-1))/n for n >= 4.
a(2^n - 1) = 2^(2^n + n - 2) if n>1. - Michael Somos, Sep 30 2022
EXAMPLE
G.f. = x + 5*x^2 + 16*x^3 + 42*x^4 + 100*x^5 + 228*x^6 + ... - Michael Somos, Sep 30 2022
MAPLE
ogf := ((1 - x)*x)/((1 - 2*x)^2*(2*x^2 - 2*x + 1));
ser := series(ogf, x, 32): seq(coeff(ser, x, n), n=0..31);
MATHEMATICA
LinearRecurrence[{6, -14, 16, -8}, {0, 1, 5, 16}, 32] (* Georg Fischer, May 08 2021 *)
PROG
(PARI) {a(n) = if(n<0, 0, polcoeff( x*(1 - x) / ((1 - 2*x)^2*(1 - 2*x + 2*x^2)), n))}; /* Michael Somos, Sep 30 2022 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Jan 12 2019
STATUS
approved