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A376113
a(0) = 1; a(n) = (1/3) * Sum_{k=1..n} (4^k-1) * a(k-1) * a(n-k).
2
1, 1, 6, 137, 11938, 4095882, 5599192492, 30588428274345, 668265444025582410, 58395039572032120897838, 20410643002515607839683651348, 28536181214271796693200339702494058, 159585939576145805663910944364491926768148, 3569877304419418296304606194938539586766279745396
OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 3 / (3 + x * A(x) - 4 * x * A(4*x)).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (1/3) Sum[(4^k - 1) a[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 13}]
nmax = 13; A[_] = 0; Do[A[x_] = 3/(3 + x A[x] - 4 x A[4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 10 2024
STATUS
approved