A385766 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x)^2 - x^2*A(x)*A'(x))).
1, 2, 9, 66, 629, 7071, 89609, 1248355, 18820831, 303879698, 5215803877, 94656100969, 1808853399445, 36282216181916, 761902799960049, 16714472406574829, 382369378451581045, 9107117241193913850, 225512045313741357841, 5798133159909683869788
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..445
Programs
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Mathematica
terms = 20; A[] = 0; Do[A[x] = 1/((1-x)*(1-x*A[x]^2-x^2*A[x]*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 2025 *)
Formula
a(n) = 1 + Sum_{i, j, k>=0 and i+j+k=n-1} (i+1) a(i) * a(j) * a(k).