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%I #31 Jul 15 2021 10:26:36
%S 1,1,10,109,1351,19612,333451,6493069,141264820,3376695763,
%T 87799365343,2465959810690,74353064138749,2393123710957813,
%U 81812390963020066,2958191064076428793,112727516544416978299,4513118224822056822772,189305466502867876489519
%N Shifts one place left under 9th-order binomial transform.
%C Previous name was: Row sums of triangle A075504 (for n>=1).
%H Muniru A Asiru, <a href="/A075508/b075508.txt">Table of n, a(n) for n = 0..108</a>
%F a(n) = Sum_{m=0..n} 9^(n-m)*S2(n,m), with S2(n,m) = A008277(n,m) (Stirling2).
%F E.g.f.: exp((exp(9*x)-1)/9).
%F O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 9*j*x). - _Ilya Gutkovskiy_, Mar 20 2018
%F a(n) ~ 9^n * n^n * exp(n/LambertW(9*n) - 1/9 - n) / (sqrt(1 + LambertW(9*n)) * LambertW(9*n)^n). - _Vaclav Kotesovec_, Jul 15 2021
%p [seq(factorial(k)*coeftayl(exp((exp(9*x)-1)/9), x = 0, k), k=0..20)]; # _Muniru A Asiru_, Mar 20 2018
%t Table[9^n BellB[n, 1/9], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 20 2015 *)
%o (GAP) List([0..20],n->Sum([0..n],m->9^(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
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