A353041 G.f. A(x) satisfies: A(x) = 1 + x * A(3*x/(1 + 2*x)) / (1 - x).

1, 1, 4, 34, 820, 62140, 14651728, 10547347384, 22950318347248, 150277943334242320, 2955664382713520203072, 174478760893191691170298912, 30905073486465684713191125079360, 16423574117627547687292156418920831936, 26184104208316120602662312616366633316565248

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f.: Sum_{k>=0} 3^(k*(k-1)/2) * (x/(1 - x))^k.

a(n) = Sum_{k=0..n} binomial(n-1,k-1) * 3^(k*(k-1)/2).

Mathematica

nmax = 14; A[_] = 0; Do[A[x_] = 1 + x A[3 x/(1 + 2 x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Sum[Binomial[n - 1, k - 1] 3^(k (k - 1)/2), {k, 0, n}], {n, 0, 14}]

Crossrefs

Cf. A006898, A047656, A135755 (partial sums), A353042.

Sequence in context: A088077 A358326 A162079 * A113231 A055621 A000860

Adjacent sequences: A353038 A353039 A353040 * A353042 A353043 A353044

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 19 2022

Status

approved