A034255 Related to quartic factorial numbers A007696.

1, 10, 120, 1560, 21216, 297024, 4243200, 61526400, 902387200, 13355330560, 199115837440, 2986737561600, 45030812467200, 681895160217600, 10364806435307520, 158063298138439680, 2417438677411430400, 37067393053641932800, 569667303771760230400, 8772876478085107548160

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn
• changed

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..833
• Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seq., Vol. 3 (2000), Article 00.2.4.
• 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

First column of triangle A048882.

Cf. A007696, A068466.

Programs

Mathematica

Rest[CoefficientList[Series[(-1+(1-16x)^(-1/4))/4,{x,0,20}],x]] (* Harvey P. Dale, May 19 2011 *)

Formula

a(n) = 4^(n-1)*A007696(n)/n!, where A007696(n) = (4*n-3)(!^4) = Product_{j=1..n} (4*j-3), n >= 1.

G.f.: (-1+(1-16*x)^(-1/4))/4.

a(n) = A048882(n, 1).

Convolution of A034385(n-1) with A025749(n), n >= 1.

D-finite with recurrence: n*a(n) + 4*(-4*n+3)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020

a(n) ~ 2^(4*n-2) * n^(-3/4) / Gamma(1/4). - Amiram Eldar, Aug 18 2025