A349016 G.f. A(x) satisfies: A(x) = 1 + x * A(-x) / (1 - x) + x * A(x)^2.

1, 2, 3, 12, 26, 125, 317, 1642, 4492, 24188, 69174, 381613, 1123923, 6304781, 18962485, 107682542, 329007674, 1885923378, 5833166568, 33685017384, 105214504816, 611241171298, 1924588709710, 11236434464097, 35617302886643, 208815253200975, 665665428686531

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

Mathematica

nmax = 26; A[_] = 0; Do[A[x_] = 1 + x A[-x]/(1 - x) + x A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[a[k] ((-1)^k + a[n - k - 1]), {k, 0, n - 1}]; Table[a[n], {n, 0, 26}]

Crossrefs

Cf. A000108, A073157, A215973, A349014, A349015.

Sequence in context: A016021 A173669 A136703 * A249490 A075269 A215602

Adjacent sequences: A349013 A349014 A349015 * A349017 A349018 A349019

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 05 2021

Status

approved