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%I #14 Aug 13 2021 21:27:39
%S 1,1,1,1,1,1,2,5,15,52,204,902,4532,26196,175320,1351296,11819348,
%T 115309534,1236465988,14419850138,181652022376,2462053028798,
%U 35834756184146,559816444117400,9389648056139010,169166236946379128,3273760080403458226,67994123544008546820
%N a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} Stirling2(n-4,k) * a(k).
%C Shifts left 4 places under Stirling transform.
%H Alois P. Heinz, <a href="/A336021/b336021.txt">Table of n, a(n) for n = 0..384</a>
%F E.g.f. A(x) satisfies A(x) = 1 + x + x^2/2 + x^3/6 + Integral( Integral( Integral( Integral A(exp(x) - 1) dx) dx) dx) dx.
%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<4, 1, b(n-4, 0)):
%p seq(a(n), n=0..27); # _Alois P. Heinz_, Aug 13 2021
%t a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 4, k] a[k], {k, 0, n - 4}]; Table[a[n], {n, 0, 27}]
%t nmax = 27; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + x^3/6 + Integrate[Integrate[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], x], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!
%o (PARI) lista(nn) = {my(va = vector(nn, k, 1)); for (n=5, nn, va[n] = sum(k=0, n-4, stirling(n-5, k, 2)*va[k+1]);); va;} \\ _Michel Marcus_, Jul 06 2020
%Y Cf. A003659, A007469, A336020, A336022.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Jul 05 2020
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