A351973 - OEIS

A351973

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

1, 0, 1, 0, 1, 1, 2, 2, 3, 4, 6, 9, 12, 18, 24, 36, 49, 72, 99, 144, 200, 289, 404, 581, 816, 1168, 1646, 2350, 3320, 4730, 6692, 9522, 13487, 19174, 27177, 38614, 54757, 77771, 110318, 156646, 222246, 315526, 447719, 635569, 901924, 1280257, 1816886, 2578911

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OFFSET

0,7

LINKS

Table of n, a(n) for n=0..47.

FORMULA

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

MATHEMATICA

a[n_]:= a[n] = (-1)^n + Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 47}]

nmax = 47; A[_] = 0; Do[A[x_] = 1/((1 + x) (1 - x A[x^2])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

CROSSREFS

Cf.A000621,A005043,A351972.