A104253 Row sums of triangle in A116925.

1, 3, 6, 11, 21, 45, 113, 339, 1221, 5273, 27237, 167985, 1235820, 10838397, 113281002, 1410702627, 20928310905, 369834091857, 7784253038081, 195135698311989, 5825657474768916, 207120610510791805, 8769156584345509398, 442116458092151729925, 26542966216935028587896

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..162

Formula

a(n) ~ c * BarnesG(n/3 + 1)^3 * BarnesG(n+1) / BarnesG(2*n/3 + 1)^3 ~ c * exp(1/12) * 3^(n^2/2) / (A * n^(1/12) * 2^(2*n^2/3 - 1/4)), where c = 5.2335188744705752675068634418929940491557563366762252523140713171090086689943... and A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 02 2021

Mathematica

Table[Sum[1 + Sum[Product[Binomial[n-1, n - s + j]/Binomial[n-1, j], {j, 0, k-1}], {k, 1, s}], {s, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Apr 02 2021 *)
Table[BarnesG[1 + n] * Sum[BarnesG[1 + k] * BarnesG[1 + n - s] * BarnesG[1 - k + s] / (BarnesG[1 - k + n] * BarnesG[1 + k + n - s] * BarnesG[1 + s]), {s, 0, n}, {k, 0, s}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 02 2021 *)

Crossrefs

Cf. A116925.

Sequence in context: A360045 A354695 A293066 * A283668 A191581 A192896

Adjacent sequences: A104250 A104251 A104252 * A104254 A104255 A104256

Keyword

nonn

Author

N. J. A. Sloane, Sep 08 2006

Status

approved