A221534 E.g.f.: Sum_{n>=0} a(n) * (cos(n*x) - sin(n*x))^n * x^n/n! = 1 + x.

1, 1, 2, 27, 968, 68865, 8252496, 1505652267, 390426582272, 136910626544673, 62531921536979200, 36122742294179711643, 25777397243775426776064, 22288717300246130379501921, 22978204666564567674247942144, 27861330789200983137890612877675

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Example

 By definition, the coefficients a(n) satisfy:
1+x = 1 + 1*(cos(x)-sin(x))*x + 2*(cos(2*x)-sin(2*x))^2*x^2/2! + 27*(cos(3*x)-sin(3*x))^3*x^3/3! + 968*(cos(4*x)-sin(4*x))^4*x^4/4! + 68865*(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)!*(-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. A218798, A221535.

Sequence in context: A251693 A182934 A078102 * A221535 A067075 A015217

Adjacent sequences: A221531 A221532 A221533 * A221535 A221536 A221537

Keyword

nonn

Author

Paul D. Hanna, Jan 19 2013

Status

approved