# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a075506 Showing 1-1 of 1 %I A075506 #31 Jul 15 2021 10:25:09 %S A075506 1,1,8,71,729,8842,125399,2026249,36458010,719866701,15453821461, %T A075506 358100141148,8899677678109,235877034446341,6634976621814472, %U A075506 197269776623577659,6177654735731310917,203136983117907790890,6994626418539177737803,251584328242318030774781 %N A075506 Shifts one place left under 7th-order binomial transform. %C A075506 Previous name was: Row sums of triangle A075502 (for n>=1). %H A075506 Muniru A Asiru, Table of n, a(n) for n = 0..110 %F A075506 a(n) = sum((7^(n-m))*S2(n,m), m=0..n), with S2(n,m) = A008277(n,m) (Stirling2). %F A075506 E.g.f.: exp((exp(7*x)-1)/7). %F A075506 O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 7*j*x). - _Ilya Gutkovskiy_, Mar 20 2018 %F A075506 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 A075506 [seq(factorial(k)*coeftayl(exp((exp(7*x)-1)/7), x = 0, k), k=0..20)]; # _Muniru A Asiru_, Mar 20 2018 %t A075506 Table[7^n BellB[n, 1/7], {n, 0, 20}] %o A075506 (GAP) List([0..20],n->Sum([0..n],m->7^(n-m)*Stirling2(n,m))); # _Muniru A Asiru_, Mar 20 2018 %Y A075506 Shifts one place left under k-th order binomial transform, k=1..10: A000110, A004211, A004212, A004213, A005011, A005012, A075506, A075507, A075508, A075509. %K A075506 nonn,easy,eigen %O A075506 0,3 %A A075506 _Wolfdieter Lang_, Oct 02 2002 %E A075506 a(0)=1 inserted and new name by _Vladimir Reshetnikov_, Oct 20 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE