A034996 Related to octo-factorial numbers A045755.

1, 36, 1632, 81600, 4308480, 235530240, 13189693440, 751812526080, 43438057062400, 2536782532444160, 149439552820346880, 8866746800673914880, 529276578255612149760, 31756594695336728985600, 1913864106972293533532160, 115788778471823758778695680, 7029059963701301121153761280

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Convolution of A034977(n-1) with A025753(n), n >= 1.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..555
• Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A045755, A034977, A025753, A034904, A203142.

Programs

Mathematica

Rest@ CoefficientList[Series[(-1 + (1 - 64*x)^(-1/8))/8, {x, 0, 14}], x] (* Michael De Vlieger, Oct 13 2019 *)

Formula

a(n) = 8^(n-1)*A045755(n)/n!, where A045755(n) = (8*n-7)!^8 = Product_{j=1..n} (8*j-7).

G.f.: (-1+(1-64*x)^(-1/8))/8.

D-finite with recurrence: n*a(n) + 8*(-8*n+7)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020

a(n) ~ 8^(2*n-1) * n^(-7/8) / Gamma(1/8). - Amiram Eldar, Aug 18 2025