OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
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.
Thomas M. Richardson, The Super Patalan Numbers, J. Int. Seq. 18 (2015), Article 15.3.3; arXiv preprint, arXiv:1410.5880 [math.CO], 2014.
FORMULA
G.f.: (11-(1-100*x)^(1/10))/10.
a(n) = 10^(n-1)*9*A035278(n-1)/n!, n >= 2, where 9*A035278(n-1) = (10*n-11)(!^10) = Product_{j=2..n} (10*j - 11). - Wolfdieter Lang
Conjecture: n*a(n) + 10*(-10*n+11)*a(n-1) = 0. - R. J. Mathar, Jul 28 2014
a(n) = 100^(n-1)*Pochhammer(9/10, n-1)/n! for n >= 1. Maple confirms this satisfies Mathar's conjecture for n >= 2 (it's not true for n=1). - Robert Israel, Oct 05 2014
a(n) ~ 100^(n-1) / (Gamma(9/10) * n^(11/10)). - Amiram Eldar, Aug 20 2025
MATHEMATICA
CoefficientList[Series[(11 -(1 - 100*x)^(1/10))/10, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)
a[n_] := 100^(n-1) * Pochhammer[9/10, n-1] / n!; a[0] = 1; Array[a, 26, 0] (* Amiram Eldar, Aug 20 2025 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!( (11 - (1-10^2*x)^(1/10))/10 )); // G. C. Greubel, Oct 30 2025
(SageMath)
def A025755(n): return 1 if n==0 else 10^(2*n-2)*rising_factorial(9/10, n-1)/factorial(n)
[A025755(n) for n in range(41)] # G. C. Greubel, Oct 30 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved