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A345178
a(0) = 0, a(1) = 1; a(n+2) = Sum_{k=0..n} Stirling2(n,k) * a(k).
2
0, 1, 0, 1, 1, 2, 8, 38, 194, 1138, 8154, 71544, 739406, 8674238, 113451160, 1648133190, 26631054962, 478633871152, 9531297220728, 208851860234540, 4997665703050398, 129765874491438094, 3639593254921626678, 109942671192206473592, 3569449102675488493032, 124319448405579907085938
OFFSET
0,6
LINKS
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
a(m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> `if`(n<2, n, b(n-2, 0)):
seq(a(n), n=0..25); # Alois P. Heinz, Aug 13 2021
MATHEMATICA
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}]
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]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 10 2021
STATUS
approved