cp's OEIS Frontend

E.g.f.: exp(x) - exp(x+1/2*x^2) - exp(x+1/5*x^5) + exp(x+1/2*x^2+1/5*x^5+1/10*x^10).

From Benedict W. J. Irwin, May 27 2016: (Start)

Let y1(0)=1, y1(1)=1,

Let -y1(n)-y1(n+1)+(n+2)*y1(n+2)=0,

Let y2(0)=1, y2(1)=1, y2(2)=1/2, y2(3)=1/6, y2(4)=1/24,

Let -y2(n)-y2(n+4)+(n+5)*y2(n+5)=0,

Let y3(0)=1, y3(1)=1, y3(2)=1, y3(3)=2/3, y3(4)=5/12, y3(5)=5/12, y3(6)=11/36, y3(7)=31/126, y3(8)=307/2016, y3(9)=1643/18144,

Let -y3(n)-y3(n+5)-y3(n+8)-y3(n+9)+(n+10)*y3(n+10)=0,

a(n) = 1+n!*(y3(n)-y2(n)-y1(n)).

(End)

E.g.f.: exp(x + 1/2*x^2) - exp(x + 1/2*x^2 + 1/4*x^4) - exp(x + 1/2*x^2 + 1/3*x^3 + 1/6*x^6) + exp(x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 + 1/6*x^6 + 1/12*x^12).

E.g.f.: - exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) + exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8 + 1/16*x^16).

E.g.f.: exp(x + 1/2*x^2 + 1/4*x^4) - exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) - exp(x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 + 1/6*x^6 + 1/12*x^12) + exp(x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 + 1/6*x^6 + 1/8*x^8 + 1/12*x^12 + 1/24*x^24).