A351161 G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).

0, 1, 0, 1, 12, 109, 900, 7309, 62280, 590185, 6402360, 78347593, 1042633908, 14648616757, 214421295132, 3266839420021, 52041902492496, 870810496011793, 15326196662766384, 283049655668743249, 5460180803581446684, 109489002283248831037, 2273856664328893182324

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..22.

Formula

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

Mathematica

nmax = 22; A[_] = 0; Do[A[x_] = x + x^2 A[x/(1 - 6 x)]/(1 - 6 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] 6^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A000995, A005012, A351028, A351053, A351057, A351128, A351132, A351152.

Sequence in context: A085797 A016161 A081200 * A016214 A037581 A177071

Adjacent sequences: A351158 A351159 A351160 * A351162 A351163 A351164

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 03 2022

Status

approved