|
%I #10 Jan 19 2013 08:42:29
%S 1,1,4,57,2072,147925,17749536,3240106485,840395708928,
%T 294739255397385,134627422799345920,77773271544276025553,
%U 55500837134575871643648,47990173549409999557055133,49475217831781002832374386688,59989657372751900405803761497805,84553864714598468031554754299887616
%N E.g.f.: Sum_{n>=0} a(n) * (cos(n*x) - sin(n*x))^n * x^n/n! = 1/(1-x).
%e By definition, the coefficients a(n) satisfy:
%e 1/(1-x) = 1 + 1*(cos(x)-sin(x))*x + 4*(cos(2*x)-sin(2*x))^2*x^2/2! + 57*(cos(3*x)-sin(3*x))^3*x^3/3! + 2072*(cos(4*x)-sin(4*x))^4*x^4/4! + 147925*(cos(5*x)-sin(5*x))^5*x^5/5! +...+ a(n)*(cos(n*x)-sin(n*x))^n*x^n/n! +...
%o (PARI) {a(n)=local(A=[1, 1], N); for(i=1, n, A=concat(A, 0); N=#A; A[N]=(N-1)!*(1-Vec(sum(m=0, N-1, A[m+1]*x^m/m!*(cos(m*x+x*O(x^N))-sin(m*x+x*O(x^N)))^m))[N])); A[n+1]}
%o for(n=0, 25, print1(a(n), ", "))
%Y Cf. A219504, A221534, A209316.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 19 2013
|
