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1, 1, 3, 5, 15, 61, 207, 881, 4491, 21493, 117543, 710021, 4266279, 28107745, 196120515, 1397747525, 10648637151, 84304440685, 688868927151, 5913133211249, 52348170504555, 479326416322933, 4557380168574135, 44560107679838549, 449806788855058407, 4680686977970550721
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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(eigensequence of the inverse of Pascal's triangle).
A014182 = expansion of exp(1-x-exp(-x)).
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LINKS
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FORMULA
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A000110 / A014182 = (1, 1, 2, 5, 15, 52, 203,...) / (1, 0, -1, 1, 2, -9, 9, 50,...).
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EXAMPLE
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A000110 = 52 = (1, 1, 3, 5, 15, 61) convolved with (1, 0, -1, 1, 2, -9)
= (61 - 5 + 3 + 2 - 9)
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MATHEMATICA
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nmax = 30; Table[a[j]/.SolveAlways[Table[Sum[a[k]*Sum[(-1)^(n-k-m)*StirlingS2[n-k+1, m+1], {m, 0, n-k}], {k, 0, n}]==BellB[n], {n, 0, nmax}], a][[1]], {j, 0, nmax}] (* Vaclav Kotesovec, Jul 26 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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