|
Search: id:A000481
|
|
|
| A000481 |
|
Stirling numbers of the second kind, S(n,5).
(Formerly M4981 N2141)
|
|
+0
7
|
|
| 1, 15, 140, 1050, 6951, 42525, 246730, 1379400, 7508501, 40075035, 210766920, 1096190550, 5652751651, 28958095545, 147589284710, 749206090500, 3791262568401
(list; graph; listen)
|
|
|
OFFSET
|
5,2
|
|
|
REFERENCES
|
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 835.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 223.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=5..200
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 348
|
|
FORMULA
|
G.f.: x^5/product(1-k*x, k=1..5). E.g.f.: ((exp(x)-1)^5)/5!.
|
|
MAPLE
|
A000481:=-1/(z-1)/(4*z-1)/(-1+3*z)/(2*z-1)/(5*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
MATHEMATICA
|
lst={}; Do[f=StirlingS2[n, 5]; AppendTo[lst, f], {n, 5, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
|
|
CROSSREFS
|
a(n)= A008277(n, 5) (Stirling2 triangle).
Cf. A008277.
Adjacent sequences: A000478 A000479 A000480 this_sequence A000482 A000483 A000484
Sequence in context: A035330 A002803 A056281 this_sequence A055903 A026859 A096046
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
