%I #31 Jul 15 2021 10:25:09
%S 1,1,8,71,729,8842,125399,2026249,36458010,719866701,15453821461,
%T 358100141148,8899677678109,235877034446341,6634976621814472,
%U 197269776623577659,6177654735731310917,203136983117907790890,6994626418539177737803,251584328242318030774781
%N Shifts one place left under 7th-order binomial transform.
%C Previous name was: Row sums of triangle A075502 (for n>=1).
%H Muniru A Asiru, <a href="/A075506/b075506.txt">Table of n, a(n) for n = 0..110</a>
%F a(n) = sum((7^(n-m))*S2(n,m), m=0..n), with S2(n,m) = A008277(n,m) (Stirling2).
%F E.g.f.: exp((exp(7*x)-1)/7).
%F O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 7*j*x). - _Ilya Gutkovskiy_, Mar 20 2018
%F a(n) ~ 7^n * n^n * exp(n/LambertW(7*n) - 1/7 - n) / (sqrt(1 + LambertW(7*n)) * LambertW(7*n)^n). - _Vaclav Kotesovec_, Jul 15 2021
%p [seq(factorial(k)*coeftayl(exp((exp(7*x)-1)/7), x = 0, k), k=0..20)]; # _Muniru A Asiru_, Mar 20 2018
%t Table[7^n BellB[n, 1/7], {n, 0, 20}]
%o (GAP) List([0..20],n->Sum([0..n],m->7^(n-m)*Stirling2(n,m))); # _Muniru A Asiru_, Mar 20 2018
%Y Shifts one place left under k-th order binomial transform, k=1..10: A000110, A004211, A004212, A004213, A005011, A005012, A075506, A075507, A075508, A075509.
%K nonn,easy,eigen
%O 0,3
%A _Wolfdieter Lang_, Oct 02 2002
%E a(0)=1 inserted and new name by _Vladimir Reshetnikov_, Oct 20 2015