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%I #29 Jul 15 2021 10:25:53
%S 1,1,9,89,1009,13457,210105,3747753,74565473,1628999841,38704241897,
%T 993034281593,27340167242321,803154583649329,25050853217628313,
%U 826165199464341705,28707262835597618369,1047731789671001235265,40053733152627299592137,1599910554128824794493593
%N Shifts one place left under 8th-order binomial transform.
%C Previous name was: Row sums of triangle A075503 (for n>=1).
%H Muniru A Asiru, <a href="/A075507/b075507.txt">Table of n, a(n) for n = 0..110</a>
%F a(n) = Sum_{m=0..n} 8^(n-m)*S2(n,m), with S2(n,m) = A008277(n,m) (Stirling2).
%F E.g.f.: exp((exp(8*x)-1)/8).
%F O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 8*j*x). - _Ilya Gutkovskiy_, Mar 20 2018
%F a(n) ~ 8^n * n^n * exp(n/LambertW(8*n) - 1/8 - n) / (sqrt(1 + LambertW(8*n)) * LambertW(8*n)^n). - _Vaclav Kotesovec_, Jul 15 2021
%p [seq(factorial(k)*coeftayl(exp((exp(8*x)-1)/8), x = 0, k), k=0..20)]; # _Muniru A Asiru_, Mar 20 2018
%t Table[8^n BellB[n, 1/8], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 20 2015 *)
%o (GAP) List([0..20],n->Sum([0..n],m->8^(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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