A034255 Related to quartic factorial numbers A007696.

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

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..833

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

Formula

a(n) = 4^(n-1)*A007696(n)/n!, A007696(n)=(4*n-3)(!^4) := product(4*j-3, j=1..n), n >= 1; G.f. (-1+(1-16*x)^(-1/4))/4.

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

Mathematica

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

Crossrefs

Cf. A007696. a(n)= A048882(n, 1) (first column of triangle).

Sequence in context: A318495 A320760 A366711 * A363310 A051582 A122420

Adjacent sequences: A034252 A034253 A034254 * A034256 A034257 A034258

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved