|
Search: id:A072597
|
|
|
| A072597 |
|
Expansion of 1/(exp(-x)-x) as exponential generating function. |
|
+0
4
|
|
| 1, 2, 7, 37, 261, 2301, 24343, 300455, 4238153, 67255273, 1185860331, 23000296155, 486655768525, 11155073325917, 275364320099807, 7282929854486431, 205462851526617489, 6158705454187353297
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Polynomials from A140749/A141412 are linked to Stirling1 (see A048594, A129841, A140749).See also P. Flajolet, X. Gourdon, B. Salvy in, available on Internet, RR-1857.pdf (preprint of unavailable Gazette des Mathematiciens 55, 1993, pp.67-78.For graph 2 see also X. Gourdon RR-1852.pdf, pp.64-65). What is the corresponding graph for A152650/A152656 =simplified A009998/A119502 linked, via A152818, to a(n), then Stirling2? [From Paul Curtz (bpcrtz(AT)free.fr), Dec 16 2008]
|
|
FORMULA
|
E.g.f.: 1/(exp(-x)-x).
a(n) = n!*Sum_{k=0..n} (n-k+1)^k/k!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 31 2003
a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling2(n, k)*A052820(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 12 2004
Recurrence : a(n+1) = 1 + sum { j=1, n, binomial(n, j)*a(j)*j } - Jon Perry (perry(AT)globalnet.co.uk), Apr 25 2005
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, n!*polcoeff(1/(exp(-x+x*O(x^n))-x), n))
|
|
CROSSREFS
|
Cf. A000110.
Sequence in context: A020040 A125191 A135164 this_sequence A125515 A135920 A001515
Adjacent sequences: A072594 A072595 A072596 this_sequence A072598 A072599 A072600
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Michael Somos, Jun 23, 2002
|
|
|
Search completed in 0.002 seconds
|
