A376134 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^k * (k+1) * a(k) * a(n-k-1).
1, 1, -1, -6, 17, 141, -660, -6688, 43837, 521755, -4412893, -60477282, 628119268, 9772644140, -120524236108, -2103803950976, 30068650440341, 582807287964375, -9477098158324107, -202143447363632090, 3686281848172281145, 85853256990102196221, -1735552985238117874788
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Sum[(-1)^k (k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 22}] nmax = 22; A[] = 0; Do[A[x] = 1/(1 - x A[-x] + x^2 A'[-x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Formula
G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(-x) + x^2 * A'(-x)).