VOOZH about

URL: https://oeis.org/A035323

⇱ A035323 - OEIS

login
A035323
Related to deca-factorial numbers A045757.
1
1, 55, 3850, 298375, 24466750, 2079673750, 181228712500, 16084048234375, 1447564341093750, 131728355039531250, 12095058053629687500, 1118792869960746093750, 104133797896346367187500, 9743948231729552929687500, 915931133782577975390625000, 86441000750730796427490234375
OFFSET
1,2
COMMENTS
Convolution of A035308(n-1) with A025755(n), n >= 1.
LINKS
Wolfdieter Lang, On generalizations of the 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.
FORMULA
a(n) = 10^(n-1)*A045757(n)/n!, where A045757(n) = (10*n-9)(!^10) = Product_{j=1..n} (10*j-9).
G.f.: (-1+(1-100*x)^(-1/10))/10.
D-finite with recurrence: n*a(n) + 10*(-10*n+9)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
a(n) ~ 10^(2*n-1) * n^(-9/10) / Gamma(1/10). - Amiram Eldar, Aug 18 2025
MATHEMATICA
Rest@ CoefficientList[Series[(-1 + (1 - 100 x)^(-1/10))/10, {x, 0, 13}], x] (* Michael De Vlieger, Oct 13 2019 *)
CROSSREFS
KEYWORD
easy,nonn
STATUS
approved