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A376126
a(n) = 1 + Sum_{k=0..n-1} (k+1)^2 * a(k) * a(n-k-1).
1
1, 2, 11, 127, 2446, 69766, 2758136, 144660949, 9742594594, 820936644105, 84720182796109, 10518406503248799, 1547501158599695053, 266325797207877471893, 53021169588315247959918, 12092601263851930181412631, 3132724961425012148414534036, 914922971820526793968713748093
OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 3 * x^2 * A'(x) - x^3 * A''(x)) ).
MATHEMATICA
a[n_] := a[n] = 1 + Sum[(k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
nmax = 17; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x] - 3 x^2 A'[x] - x^3 A''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 11 2024
STATUS
approved