A392468 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 2*x)^2) / (1 - 2*x).

1, 1, 3, 13, 75, 533, 4451, 42509, 455643, 5401957, 70032627, 983920925, 14871639723, 240356538165, 4132531218947, 75253340888237, 1445870691434491, 29213295614974597, 618875804638786963, 13710867155632244157, 316921080222839442379, 7626936425442561535829, 190737898451017682528163

Offset

0,3

Links

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

Formula

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

Mathematica

nmax = 22; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - 2 x)^2]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + k - 1, n - k - 1] 2^(n - k - 1) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A000110, A004211, A005493, A007405, A125273, A390837, A392532, A392538, A393535, A393536.

Sequence in context: A334637 A007178 A173990 * A276924 A343788 A276895

Adjacent sequences: A392465 A392466 A392467 * A392469 A392470 A392471

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2026

Status

approved