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A000770
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Stirling numbers of the second kind, S(n,6).
(Formerly M5112 N2215)
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7
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1, 21, 266, 2646, 22827, 179487, 1323652, 9321312, 63436373, 420693273, 2734926558, 17505749898, 110687251039, 693081601779, 4306078895384, 26585679462804, 163305339345225, 998969857983405, 6090236036084530, 37026417000002430, 224595186974125331
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,2
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=6..200
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 349
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.
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FORMULA
| G.f.: x^6/product(1-k*x, k=1..6). E.g.f. ((exp(x)-1)^6)/6!.
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MAPLE
| A000770:=1/(z-1)/(6*z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| lst={}; Do[f=StirlingS2[n, 6]; AppendTo[lst, f], {n, 6, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
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CROSSREFS
| a(n)= A008277(n, 6) (Stirling2 triangle).
Cf. A008277.
Sequence in context: A092794 A133717 A056282 * A133105 A032535 A022745
Adjacent sequences: A000767 A000768 A000769 * A000771 A000772 A000773
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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