|
Search: id:A091046
|
|
|
| A091046 |
|
Stirling transform of first differences of Bell numbers (A005493), if offset zero. In Maple notation: a(n)=sum(stirling2(n,k)*A005493(k), k=1..n), n=1,2.... |
|
+0
1
|
|
| 1, 4, 20, 119, 817, 6338, 54707, 519184, 5366097, 59934937, 718748131, 9203953921, 125268224954, 1804750726306, 27426230051634, 438260834123607, 7343677070172330, 128716143768613600, 2354633702684629141
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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
|
|
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....
|
|
CROSSREFS
|
Cf. A005493.
Cf. A039810.
Adjacent sequences: A091043 A091044 A091045 this_sequence A091047 A091048 A091049
Sequence in context: A078944 A127088 A128236 this_sequence A101055 A013197 A089498
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Karol A. Penson (penson(AT)lptl.jussieu.fr), Dec 15 2003
|
|
|
Search completed in 0.002 seconds
|
