A367723 E.g.f. satisfies A(x) = exp(x*A(-x^4)).
1, 1, 1, 1, 1, -119, -719, -2519, -6719, 166321, 3598561, 29882161, 159572161, -389343239, -55939643759, -974399385959, -9282412863359, -46891283580959, 1814094098389441, 67045782535457761, 1076141148146824321, 61735522719009663721, 1058382395842664859121
Offset: 0
Keywords
Programs
-
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=0, (i-1)\4, (-1)^j*(4*j+1)*v[j+1]*v[i-4*j]/(j!*(i-1-4*j)!))); v;
Formula
a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/4)} (-1)^k * (4*k+1) * a(k) * a(n-1-4*k) / (k! * (n-1-4*k)!).