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A375393
a(0) = 1; a(n) = Sum_{k=0..n-1} (4*k+3) * a(k) * a(n-k-1).
2
1, 3, 30, 483, 10314, 268686, 8167068, 281975715, 10863651474, 461227101210, 21377716429860, 1073816307452430, 58106804389870500, 3370330005649001532, 208635817503306332088, 13731856676157543219747, 957698874584753026878306, 70562301536089812703526370, 5477354759932929856218644820
OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 + 3 * x * A(x)^2 + 4 * x^2 * A'(x) * A(x).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[(4 k + 3) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[_] = 0; Do[A[x_] = 1 + 3 x A[x]^2 + 4 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 09 2024
STATUS
approved