A351150 G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 4*x)) / (1 - 4*x).

1, 0, 1, 4, 17, 80, 433, 2724, 19489, 153536, 1301601, 11754084, 112802097, 1150079056, 12437130001, 142144768324, 1709041379393, 21522252928000, 282920962675905, 3873124754702660, 55125031662585425, 814541756986322128, 12477752083406752881, 197861190429889969252

Offset: 0

Author

Ilya Gutkovskiy, Feb 02 2022

Keywords

• nonn

Comments

Shifts 2 places left under 4th-order binomial transform.

Crossrefs

Cf. A000994, A004213, A351050, A351143, A351144, A351151, A351152.

Programs

Mathematica

nmax = 23; A[] = 0; Do[A[x] = 1 + x^2 A[x/(1 - 4 x)]/(1 - 4 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[Binomial[n - 2, k] 4^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 23}]

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 4^k * a(n-k-2).