cp's OEIS Frontend

A345178 a(0) = 0, a(1) = 1; a(n+2) = Sum_{k=0..n} Stirling2(n,k) * a(k).

%I A345178 #7 Aug 13 2021 21:22:26
%S A345178 0,1,0,1,1,2,8,38,194,1138,8154,71544,739406,8674238,113451160,
%T A345178 1648133190,26631054962,478633871152,9531297220728,208851860234540,
%U A345178 4997665703050398,129765874491438094,3639593254921626678,109942671192206473592,3569449102675488493032,124319448405579907085938
%N A345178 a(0) = 0, a(1) = 1; a(n+2) = Sum_{k=0..n} Stirling2(n,k) * a(k).
%H A345178 Alois P. Heinz, <a href="/A345178/b345178.txt">Table of n, a(n) for n = 0..355</a>
%p A345178 b:= proc(n, m) option remember; `if`(n=0,
%p A345178       a(m), m*b(n-1, m)+b(n-1, m+1))
%p A345178     end:
%p A345178 a:= n-> `if`(n<2, n, b(n-2, 0)):
%p A345178 seq(a(n), n=0..25);  # _Alois P. Heinz_, Aug 13 2021
%t A345178 a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]
%t A345178 nmax = 25; A[_] = 0; Do[A[x_] = x + Normal[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], x], x] + O[x]^(nmax + 1)], nmax]; CoefficientList[A[x], x] Range[0, nmax]!
%Y A345178 Cf. A000995, A003659, A007469, A345177.
%K A345178 nonn
%O A345178 0,6
%A A345178 _Ilya Gutkovskiy_, Jun 10 2021