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A393135

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

1, 1, -1, -2, 4, 9, -21, -49, 125, 299, -803, -1952, 5426, 13343, -38011, -94282, 273572, 683123, -2010715, -5047774, 15028540, 37893371, -113878471, -288182037, 872829205, 2215587797, -6754828309, -17191614136, 52710331950, 134458267665, -414279102317

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..30.

FORMULA

a(0) = 1, for n > 0: a(n) = Sum_{j=0..n-1} Sum_{i=0..j} (-1)^j * a(i) * a(j-i).

MATHEMATICA

nmax = 30; A[_] = 0; Do[A[x_] = 1 + x A[-x]^2/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[0] = 1; a[n_] := a[n] = Sum[Sum[(-1)^j a[i] a[j - i], {i, 0, j}], {j, 0, n - 1}]; Table[a[n], {n, 0, 30}]

CROSSREFS

Cf. A001006, A002212, A007440, A090192, A108623, A108624, A143045, A371888.