A367722 E.g.f. satisfies A(x) = exp(x*A(-x^3)).
1, 1, 1, 1, -23, -119, -359, 1681, 38641, 269137, 599761, -22461119, -347288039, -8704873319, -73184815703, 16491842641, 26323288948321, 725566429691041, 7867441656997921, -20568394299884543, -4768992217846599479, -108339469662214468439
Offset: 0
Keywords
Programs
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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)\3, (-1)^j*(3*j+1)*v[j+1]*v[i-3*j]/(j!*(i-1-3*j)!))); v;
Formula
a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/3)} (-1)^k * (3*k+1) * a(k) * a(n-1-3*k) / (k! * (n-1-3*k)!).
Comments