A209317 E.g.f.: Sum_{n>=0} a(n) * (cos(n*x) - sin(n*x))^n * x^n/n! = 1/(1-x).

1, 1, 4, 57, 2072, 147925, 17749536, 3240106485, 840395708928, 294739255397385, 134627422799345920, 77773271544276025553, 55500837134575871643648, 47990173549409999557055133, 49475217831781002832374386688, 59989657372751900405803761497805, 84553864714598468031554754299887616

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Example

By definition, the coefficients a(n) satisfy:
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! +...

Prog

(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]}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A219504, A221534, A209316.

Sequence in context: A299459 A300103 A358687 * A231491 A240887 A209316

Adjacent sequences: A209314 A209315 A209316 * A209318 A209319 A209320

Keyword

nonn

Author

Paul D. Hanna, Jan 19 2013

Status

approved