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
Keywords
Programs
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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 *)
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)!).