A345177 - OEIS

%I #9 Aug 13 2021 21:20:25

%S 1,0,1,0,1,3,8,28,149,1029,8039,69375,675541,7584630,98484836,

%T 1457695370,24117255106,439505090491,8756668806615,190293641816660,

%U 4508138040317573,116298682305458460,3258081214212853975,98709283556190931672,3219222306795403565116,112538217720491999726102

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

%H Alois P. Heinz, <a href="/A345177/b345177.txt">Table of n, a(n) for n = 0..355</a>

%p b:= proc(n, m) option remember; `if`(n=0,

%p       a(m), m*b(n-1, m)+b(n-1, m+1))

%p     end:

%p a:= n-> `if`(n<2, 1-n, b(n-2, 0)):

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Aug 13 2021

%t a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[StirlingS2[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]

%t nmax = 25; A[_] = 0; Do[A[x_] = 1 + 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 Cf. A000994, A003659, A007469, A345178.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Jun 10 2021