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

0,3

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..410

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

Maple

seq(10^n*BellB(n, 1/10), n=0..18); # Peter Luschny, Oct 20 2015
# Alternative:
b:= proc(n, m) option remember;
     `if`(n=0, 1, 10*m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..22);  # Alois P. Heinz, Jun 24 2026

Mathematica

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

Crossrefs

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

Sequence in context: A015606 A077417 A082148 * A061113 A261689 A101334

Adjacent sequences: A075506 A075507 A075508 * A075510 A075511 A075512

Keyword

nonn,easy,eigen,changed

Author

Wolfdieter Lang, Oct 02 2002

Extensions

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

Status

approved