OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x * A(x)^2 + 2 * x^2 * A(x) * A'(x) + x^3 * A(x) * A''(x) / 2.
MAPLE
A351798 := proc(n)
option remember;
if n = 0 then
1;
else
add((1+k)*(2+k)*procname(k)*procname(n-k-1), k=0..n-1) ;
%/2 ;
end if;
end proc:
seq(A351798(n), n=0..30) ; # R. J. Mathar, Aug 19 2022
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (1/2) Sum[(k + 1) (k + 2) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[_] = 0; Do[A[x_] = 1 + x A[x]^2 + 2 x^2 A[x] A'[x] + x^3 A[x] A''[x]/2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 19 2022
STATUS
approved