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A336020 a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} Stirling2(n-3,k) * a(k). 2

%I

%S 1,1,1,1,1,2,5,15,53,222,1115,6698,47243,382187,3480048,35251942,

%T 394839407,4875966656,66282636371,989985346269,16198580140543,

%U 289168351452220,5604120791540468,117309414122840454,2639927837211705159,63618153549702851338

%N a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} Stirling2(n-3,k) * a(k).

%C Shifts left 3 places under Stirling transform.

%F E.g.f. A(x) satisfies A(x) = 1 + x + x^2/2 + Integral( Integral( Integral A(exp(x) - 1) dx) dx) dx.

%t a[0] = a[1] = a[2] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 25}]

%t nmax = 25; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + Integrate[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], 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=4, nn, va[n] = sum(k=0, n-3, stirling(n-4, k, 2)*va[k+1]);); va;} \\ _Michel Marcus_, Jul 06 2020

%Y Cf. A003659, A007469, A336021, A336022.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Jul 05 2020

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)