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A348878
G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(2*x)).
4
1, 1, 2, 5, 17, 74, 429, 3297, 34578, 495573, 9888497, 274123802, 10685538941, 583079000129, 44945515778914, 4867082587900837, 746167748281132753, 160981861948404281578, 49223569713040994430285, 21198824279482430844823713, 12946110661470835825027893426
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} 2^k * a(k) * a(n-k-2).
a(n) ~ c * 2^(n*(n-2)/4), where c = 10.492153305884170498003413429333844276557493974205102819840538218355... - Vaclav Kotesovec, Nov 03 2021
MATHEMATICA
nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - x - x^2 A[2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[2^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 02 2021
STATUS
approved