A034904 Related to sept-factorial numbers A045754.

1, 28, 980, 37730, 1531838, 64337196, 2766499428, 121034349975, 5365856182225, 240390356963680, 10861273400995360, 494187939745288880, 22618601857572837200, 1040455685448350511200, 48069052667713793617440, 2229202317465227179008780, 103723472536176158740937940

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Convolution of A034835(n-1) with A025752(n), n >= 1.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..594
• 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. A025752, A034835, A045754, A220086.

Programs

Mathematica

CoefficientList[Series[(Power[1-49x, (-7)^-1]-1)/7,{x,0,30}],x] (* Harvey P. Dale, Aug 23 2011 *)

Formula

a(n) = 7^(n-1)*A045754(n)/n!, where A045754(n) = (7*n-6)(!^7) = Product_{j=1..n} (7*j-6).

G.f.: (-1+(1-49*x)^(-1/7))/7.

D-finite with recurrence: n*a(n) + 7*(-7*n+6)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020

a(n) ~ 7^(2*n-1) * n^(-6/7) / Gamma(1/7). - Amiram Eldar, Aug 18 2025