A385687 E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^2 ).

1, 1, 1, 7, 25, 341, 2161, 44115, 404209, 11010025, 132273601, 4508793983, 67085545033, 2747071330173, 48765277295281, 2331905267846731, 48106649137922017, 2631174441142423505, 61862217319644572161, 3809106344377237185399, 100542158725584301036921

Offset: 0

Author

Seiichi Manyama, Jul 06 2025

Keywords

• nonn

Crossrefs

Cf. A058014, A385688.

Cf. A143546, A360987, A385690.

Programs

Mathematica

terms = 21;  A[] = 1; Do[A[x] = Exp[x*((A[x] + A[-x])/2)^2] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Jul 07 2025 *)

Formula

E.g.f. A(x) satisfies A(-x) = 1/A(x).

a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k>=0 and i+2*j+2*k=n-1} (n-i) * a(i) * a(2*j) * a(2*k)/(i! * (2*j)! * (2*k)!).