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Related to octo-factorial numbers A045755.
2

%I #14 Jan 30 2020 21:29:14

%S 1,36,1632,81600,4308480,235530240,13189693440,751812526080,

%T 43438057062400,2536782532444160,149439552820346880,

%U 8866746800673914880,529276578255612149760,31756594695336728985600

%N Related to octo-factorial numbers A045755.

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

%H Michael De Vlieger, <a href="/A034996/b034996.txt">Table of n, a(n) for n = 1..555</a>

%H Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F a(n) = 8^(n-1)*A045755(n)/n!, A045755(n)=(8*n-7)!^8 := product(8*j-7, j=1..n); G.f. (-1+(1-64*x)^(-1/8))/8.

%F D-finite with recurrence: n*a(n) +8*(-8*n+7)*a(n-1)=0. - _R. J. Mathar_, Jan 28 2020

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

%Y Cf. A045755, A034977, A025753, A034904.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_