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A144792
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EXP transform of A140585.
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1
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1, 5, 33, 282, 2938, 36029, 507440, 8058990, 142315830, 2763775025, 58498072273, 1339545500214, 32980132065364, 868417100538399, 24344702489881998, 723694354351500431, 22733368105181643193, 752291980101845144878
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Stirling transform of A143463.
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FORMULA
| E.g.f: (1/exp(1)) exp( 1 / prod_{k=1}^{inf} (1 - (exp(x)-1)^k / k!) ).
a(n) = sum_{k=1}^{n} C(n-1,k-1) A140585(k) a(n-k).
With S2(n,k) as the Stirling number of the second kind we have
a(n) = sum_{k=1}^{n} A143463(n) S2(n,k).
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MAPLE
| with (numtheory): with (combinat): b:= proc(k) option remember; add (d/d!^(k/d), d=divisors(k)) end: c:= proc(n) option remember; `if` (n=0, 1, add ((n-1)!/ (n-k)!* b(k)* c(n-k), k=1..n)) end: aa:= n-> add (stirling2 (n, k) * c(k), k=1..n): a:= proc(n) option remember; `if` (n=0, 1, aa(n)+ add (binomial (n-1, k-1) *aa(k) *a(n-k), k=1..n-1)) end: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008]
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CROSSREFS
| A140585, A143463.
Sequence in context: A049377 A129890 A120733 * A001828 A084845 A198079
Adjacent sequences: A144789 A144790 A144791 * A144793 A144794 A144795
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KEYWORD
| nonn
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AUTHOR
| Thomas Wieder (thomas.wieder(AT)t-online.de), Sep 21 2008
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008
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