A385690 E.g.f. A(x) satisfies A(x) = exp( x*A(x)*(A(x) + A(-x))/2 ).

1, 1, 3, 25, 233, 3901, 62707, 1591493, 36539953, 1246111705, 37259797091, 1597211237425, 58891746904729, 3041999861503253, 133421178853319827, 8066042741507516701, 410229480337750129889, 28415048957473232282161, 1644249408980809155863491

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

terms = 19;  A[_] = 1; Do[A[x_] = Exp[x*A[x]*(A[x] + A[-x])/2] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0, terms-1]! (* Stefano Spezia, Jul 07 2025 *)

Crossrefs

Cf. A217138, A385687, A385692.

Sequence in context: A118726 A372458 A066221 * A370280 A367786 A332468

Adjacent sequences: A385687 A385688 A385689 * A385691 A385692 A385693

Keyword

nonn

Author

Seiichi Manyama, Jul 07 2025

Status

approved