A376135 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^k * (2*k+1) * a(k) * a(n-k-1).

1, 1, -2, -15, 86, 1030, -9844, -156219, 2098406, 41282298, -716119260, -16837011158, 358425572604, 9820300812556, -247923816153128, -7765514675946195, 226869417798485382, 8001626352728559218, -265582398152349968716, -10419379442081103988738

Offset: 0

Author

Ilya Gutkovskiy, Sep 11 2024

Keywords

• sign

Crossrefs

Cf. A000699, A090192, A105523, A376134, A376137.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-1)^k (2 k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; A[] = 0; Do[A[x] = 1/(1 - x A[-x] + 2 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) + 2 * x^2 * A'(-x)).