A351152 G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).

1, 0, 1, 6, 37, 240, 1693, 13446, 122329, 1261104, 14332681, 175123446, 2267871517, 30981705984, 446571784261, 6798161166486, 109220619908593, 1846729159654560, 32726973173941585, 605358657750562470, 11648701234354836565, 232655173657593759312

Offset

0,4

Comments

Shifts 2 places left under 6th-order binomial transform.

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 6^k * a(n-k-2).

Mathematica

nmax = 21; A[_] = 0; Do[A[x_] = 1 + x^2 A[x/(1 - 6 x)]/(1 - 6 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] 6^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A000994, A005012, A351057, A351143, A351144, A351150, A351151.

Sequence in context: A005389 A080954 A271905 * A355957 A073013 A192238

Adjacent sequences: A351149 A351150 A351151 * A351153 A351154 A351155

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 02 2022

Status

approved