# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a346417 Showing 1-1 of 1 %I A346417 #12 Aug 06 2021 13:58:12 %S A346417 1,2,10,66,538,5186,57402,714594,9853978,148774914,2436823034, %T A346417 42979319202,811254807770,16302732719682,347248840767162, %U A346417 7809649226242530,184831773033020826,4589793199157616770,119272846472231229818,3235960069037751550498,91466308730323104617050 %N A346417 E.g.f.: exp(exp(2*(exp(x) - 1)) - 1). %H A346417 Alois P. Heinz, Table of n, a(n) for n = 0..449 %F A346417 a(n) = Sum_{k=0..n} Stirling2(n,k) * 2^k * Bell(k). %F A346417 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A001861(k) * a(n-k). %p A346417 b:= proc(n, t, m) option remember; `if`(n=0, `if`(t=1, 1, %p A346417 b(m, 1, 0)*2^m) , m*b(n-1, t, m)+b(n-1, t, m+1)) %p A346417 end: %p A346417 a:= n-> b(n, 0$2): %p A346417 seq(a(n), n=0..20); # _Alois P. Heinz_, Aug 06 2021 %t A346417 nmax = 20; CoefficientList[Series[Exp[Exp[2 (Exp[x] - 1)] - 1], {x, 0, nmax}], x] Range[0, nmax]! %t A346417 Table[Sum[StirlingS2[n, k] 2^k BellB[k], {k, 0, n}], {n, 0, 20}] %t A346417 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] BellB[k, 2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}] %o A346417 (PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(exp(2*(exp(x) - 1)) - 1))) \\ _Michel Marcus_, Jul 19 2021 %Y A346417 Cf. A000258, A000898, A001861, A055882, A126390, A136658. %K A346417 nonn %O A346417 0,2 %A A346417 _Ilya Gutkovskiy_, Jul 16 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE