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A348880
G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(4*x)).
3
1, 1, 2, 7, 45, 540, 12645, 578965, 52968266, 9592378291, 3490570329073, 2521575506955308, 3665174976025818601, 10583587128179171478201, 61512603105342112799632050, 710375545029057279438117199695, 16513584476995892580457952423234565
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} 4^k * a(k) * a(n-k-2).
a(n) ~ c * 2^(n*(n-2)/2), where c = 3.18049189724646501466385558274654521200715578089919192312230814532162... - Vaclav Kotesovec, Nov 03 2021
MATHEMATICA
nmax = 16; A[_] = 0; Do[A[x_] = 1/(1 - x - x^2 A[4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[4^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 16}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 02 2021
STATUS
approved