A367722 -id:A367722 - cp's OEIS frontend

A367721 E.g.f. satisfies A(x) = exp(x*A(-x^2)).

1, 1, 1, -5, -23, 1, 601, 7771, 26545, -401183, -6965999, -42828389, 528611161, 15543020065, 141983039017, -2393449681349, -83586615493919, -708151768946879, 15447932991283105, 635290179334026427, 7146984268771158601, -162583738763505944639

Offset: 0

Seiichi Manyama, Nov 28 2023

sign

Cf. A141369, A367722, A367723.

Cf. A138292.

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)\2, (-1)^j*(2*j+1)*v[j+1]*v[i-2*j]/(j!*(i-1-2*j)!))); v;

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * a(k) * a(n-1-2*k) / (k! * (n-1-2*k)!).

A367723 E.g.f. satisfies A(x) = exp(x*A(-x^4)).

Original entry on oeis.org

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

Seiichi Manyama, Nov 28 2023

sign

Cf. A141369, A367721, A367722.

Cf. A367720.

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;

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)!).

cp's OEIS Frontend

A367721 E.g.f. satisfies A(x) = exp(x*A(-x^2)).

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