A351143 G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 2*x)) / (1 - 2*x).

1, 0, 1, 2, 5, 16, 61, 258, 1177, 5776, 30537, 173394, 1050045, 6732608, 45459493, 322141106, 2390075249, 18525967328, 149684238801, 1257802518754, 10969260208565, 99100423076912, 926030783479629, 8937741026924450, 88988433270106249, 912906193294355952

Offset

0,4

Comments

Shifts 2 places left under 2nd-order binomial transform.

Links

Table of n, a(n) for n=0..25.

Formula

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

Mathematica

nmax = 25; A[_] = 0; Do[A[x_] = 1 + x^2 A[x/(1 - 2 x)]/(1 - 2 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] 2^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000994, A004211, A007472, A351144, A351150, A351151, A351152.

Sequence in context: A370797 A307228 A104858 * A303058 A322616 A178123

Adjacent sequences: A351140 A351141 A351142 * A351144 A351145 A351146

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 02 2022

Status

approved