A392532 G.f. A(x) satisfies: A(x) = 1 + x * A(2*x/(1 - x)^2) / (1 - x)^2.

1, 1, 4, 27, 336, 7485, 302028, 22527767, 3174112032, 860830383001, 455774790482644, 475669638563475699, 984532608418927789552, 4056144440301146818242325, 33333077239591357063936218268, 547060937677964735150346948379055, 17942490183726140248811670424624773696

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Mathematica

nmax = 16; A[_] = 0; Do[A[x_] = 1 + x A[2 x/(1 - x)^2]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + k, n - k - 1] 2^k a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

Crossrefs

Cf. A000110, A040027, A125273, A125274, A126443, A352859, A390837, A392468, A392538, A393535, A393536.

Sequence in context: A221411 A304654 A203202 * A385548 A320961 A239726

Adjacent sequences: A392529 A392530 A392531 * A392533 A392534 A392535

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2026

Status

approved