A346078 -id:A346078 - cp's OEIS frontend

A346079 G.f. A(x) satisfies: A(x) = x - x^2 * A(x/(1 - x)) / (1 - x).

0, 1, 0, -1, -2, -2, 2, 17, 54, 109, 54, -796, -5000, -19499, -52252, -44617, 577554, 5071906, 27330978, 108557573, 263947354, -453137963, -11252508862, -92193933208, -545809325184, -2441788385255, -6271647457176, 22814756330975, 492197181810550, 4609129908957190

Offset: 0

Ilya Gutkovskiy, Jul 04 2021

sign

Cf. A000587, A000995, A336970, A346078.

nmax = 29; A[] = 0; Do[A[x] = x - x^2 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[1] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 29}]

a(0) = 0, a(1) = 1; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k).

A351879 a(0) = a(1) = 1; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k) * a(n-k-2).

Original entry on oeis.org

1, 1, -1, -2, 0, 10, 10, -60, -220, 400, 4200, 2200, -90200, -290400, 1892000, 15796000, -24024000, -775676000, -1592492000, 36509880000, 240055640000, -1435950560000, -23703057840000, 7376731120000, 2082346354000000, 9478853472000000, -162472029808000000

Offset: 0

Ilya Gutkovskiy, Feb 23 2022

sign

Cf. A007558, A307374, A346078.

a[0] = a[1] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]

E.g.f. A(x) satisfies: A(x) = 1 + x - Integral( Integral A(x)^2 dx) dx.

cp's OEIS Frontend

A346079 G.f. A(x) satisfies: A(x) = x - x^2 * A(x/(1 - x)) / (1 - x).

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