A075509 Shifts one place left under 10th-order binomial transform.

1, 1, 11, 131, 1761, 27601, 506651, 10674211, 251686881, 6524202561, 183991725451, 5605930566051, 183428104316161, 6409252239788881, 237948848526923611, 9346097294356706051, 386966245108218203201, 16836505067572362863361, 767645305770283165781131

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy
• eigen

Comments

Previous name was: a(n) are row sums of triangle A075505 (for n>=1).

Crossrefs

Shifts one place left under k-th order binomial transform, k=1..10: A000110, A004211, A004212, A004213, A005011, A005012, A075506, A075507, A075508, A075509.

Programs

Maple

seq(10^n*BellB(n, 1/10), n=0..18); # Peter Luschny, Oct 20 2015

Mathematica

Table[10^n BellB[n, 1/10], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *)

Formula

a(n) = Sum_{m=0..n} 10^(n-m)*S2(n,m) with S2(n,m) = A048993(n,m) (Stirling2).

E.g.f.: exp((exp(10*x)-1)/10).

O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 10*j*x). - Ilya Gutkovskiy, Mar 21 2018

a(n) ~ 10^n * n^n * exp(n/LambertW(10*n) - 1/10 - n) / (sqrt(1 + LambertW(10*n)) * LambertW(10*n)^n). - Vaclav Kotesovec, Jul 15 2021

Extensions

a(0)=1 inserted and new name by Vladimir Reshetnikov, Oct 20 2015