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A091046
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Stirling transform of first differences of Bell numbers (A005493), if offset zero: a(n) = sum_{k=1..n} A008277(n,k)*A005493(k).
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1, 4, 20, 119, 817, 6338, 54707, 519184, 5366097, 59934937, 718748131, 9203953921, 125268224954, 1804750726306, 27426230051634, 438260834123607, 7343677070172330, 128716143768613600, 2354633702684629141
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equals A039810 * [1,2,3,...], i.e. the square of the Stirling2 triangle and the natural number vector. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 31 2008
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FORMULA
| Egf: (exp(exp(x)-1)-1)*exp(exp(exp(x)-1)-1) Representation as an infinite sum (Dobinski-type relation): a(n)=exp(exp(-1)-1)*sum(p^n*((sum((stirling2(p+1, k)-stirling2(p, k))*exp(-k), k=1..p)+exp(-(p+1)))/p!), p=1..infinity), n=1, 2....
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CROSSREFS
| Cf. A005493, A039810.
Sequence in context: A190194 A127088 A128236 * A101055 A013197 A089498
Adjacent sequences: A091043 A091044 A091045 * A091047 A091048 A091049
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Dec 15 2003
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