A351938 - OEIS

A351938

a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..floor((n-1)/2)} a(k) * a(n-2*k-1).

1, 1, 1, 3, 5, 9, 17, 35, 65, 125, 241, 463, 885, 1701, 3265, 6271, 12033, 23105, 44353, 85147, 163445, 313777, 602353, 1156339, 2219809, 4261389, 8180561, 15704215, 30147333, 57873821, 111100225, 213278943, 409431169, 785984353, 1508852673, 2896541859

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

FORMULA

G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(x^2)).

MATHEMATICA

a[0] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 35}]

nmax = 35; A[_] = 0; Do[A[x_] = 1/(1 + x - 2 x A[x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

CROSSREFS

Cf. A000621, A001003, A319436, A349365.