A351143 - OEIS

%I #6 Feb 03 2022 10:43:25

%S 1,0,1,2,5,16,61,258,1177,5776,30537,173394,1050045,6732608,45459493,

%T 322141106,2390075249,18525967328,149684238801,1257802518754,

%U 10969260208565,99100423076912,926030783479629,8937741026924450,88988433270106249,912906193294355952

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

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

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

%t 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]

%t 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}]

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

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Feb 02 2022