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A376112
a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} (3^k-1) * a(k-1) * a(n-k).
2
1, 1, 5, 74, 3119, 384099, 140605620, 153966205482, 505318125737963, 4973847408741044519, 146857822147450491641165, 13007931631590001724722114996, 3456493610037973055076316970551876, 2755388815749774181719259556096183210356, 6589473777446361501832833785593366614276353520
OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 2 / (2 + x * A(x) - 3 * x * A(3*x)).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (1/2) Sum[(3^k - 1) a[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 14}]
nmax = 14; A[_] = 0; Do[A[x_] = 2/(2 + x A[x] - 3 x A[3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 10 2024
STATUS
approved