A307875 G.f. A(x) satisfies: A(x) = 1 + x*(1 + x*A(x/(1 - x)^2)/(1 - x)^2).

1, 1, 1, 3, 8, 23, 78, 308, 1343, 6288, 31520, 169556, 976219, 5974381, 38597158, 262016556, 1864047379, 13870571346, 107732190252, 871392244426, 7323432971279, 63823847508765, 575833492837041, 5370836704825787, 51720220231890625, 513595474725399215, 5253091234710411001

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

Recurrence: a(n+1) = Sum_{k=0..n} binomial(n+k,2*k+1)*a(k).

Mathematica

terms = 26; A[_] = 0; Do[A[x_] = 1 + x (1 + x A[x/(1 - x)^2]/(1 - x)^2) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = Sum[Binomial[n + k - 1, 2 k + 1] a[k], {k, 0, n - 1}]; a[0] = 1; a[1] = 1; Table[a[n], {n, 0, 26}]

Crossrefs

Cf. A000110, A007476, A040027.

Sequence in context: A189359 A125782 A343176 * A321730 A047143 A148779

Adjacent sequences: A307872 A307873 A307874 * A307876 A307877 A307878

Keyword

nonn

Author

Ilya Gutkovskiy, May 02 2019

Status

approved