A376135 -id:A376135 - cp's OEIS frontend

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

Ilya Gutkovskiy, Sep 11 2024

sign

Cf. A088716, A090192, A105523, A376135, A376137.

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]

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

A376137 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^k * (k+1)^2 * a(k) * a(n-k-1).

Original entry on oeis.org

1, 1, -3, -34, 495, 13631, -467404, -23984426, 1490938299, 123999435015, -12164649041259, -1497474725212924, 212746558833692052, 36393896155519042476, -7062273474686464802160, -1603475573855830444120802, 407344895625777134555939139, 118552169162473363108837155199, -38177398083353809033748641523305

Offset: 0

Ilya Gutkovskiy, Sep 11 2024

sign

Cf. A090192, A105523, A376095, A376134, A376135.

a[0] = 1; a[n_] := a[n] = Sum[(-1)^k (k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[] = 0; Do[A[x] = 1/(1 - x A[-x] + 3 x^2 A'[-x] - x^3 A''[-x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(-x) + 3 * x^2 * A'(-x) - x^3 * A''(-x)).

cp's OEIS Frontend

A376134 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^k * (k+1) * a(k) * a(n-k-1).

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