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Search: id:A002050
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| A002050 |
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Number of simplices in barycentric subdivision of n-simplex.
(Formerly M3939 N1622)
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+0
8
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| 0, 1, 5, 25, 149, 1081, 9365, 94585, 1091669, 14174521, 204495125, 3245265145, 56183135189, 1053716696761, 21282685940885, 460566381955705, 10631309363962709, 260741534058271801, 6771069326513690645
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Stirling transform of A052849(n)=[1,4,12,48,240,...] is a(n)=[1,5,25,149,1081,..]. - Michael Somos Mar 04 2004
Stirling transform of A000142(n-1)=[0,1,2,6,24,...] is a(n-1)=[0,1,5,25,149,...]. - Michael Somos Mar 04 2004
Stirling transform of 2*A005359(n-1)=[1,0,4,0,48,0,...] is a(n-1)=[1,1,5,25,149,...]. - Michael Somos Mar 04 2004
"Stirling-Bernoulli transform" of A000225. - Paul Barry (pbarry(AT)wit.ie), Apr 20 2005
a(n) is the number of nonempty words that can be formed from an alphabet of nonempty subsets of [n] so that the letters in each word are pairwise disjoint. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 12 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
G. J. Simmons, A combinatorial problem associated with a family of combination locks, Math. Mag., 37 (1964), 127-132 (but there are errors).
J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 149
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FORMULA
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E.g.f.: (exp(2x)-exp(x))/(2-exp(x)).
a(n)=sum{k=0..n, (-1)^(n-k)k!*S2(n, k)(2^k-1)}. - Paul Barry (pbarry(AT)wit.ie), Apr 20 2005
a(n)= Sum{k=1...n,Binomial(n,k)*A000670(k)} [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 12 2009]
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MATHEMATICA
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Table[Sum[Binomial[n, i]*Sum[StirlingS2[i, k]*k!, {k, 1, i}], {i, 1, n}], {n, 0, 20}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 12 2009]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*polcoeff(subst((y+y^2)/(1-y), y, exp(x+x*O(x^n))-1), n))
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CROSSREFS
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a(n) = A000629(n) - 1.
Adjacent sequences: A002047 A002048 A002049 this_sequence A002051 A002052 A002053
Sequence in context: A121639 A098349 A098212 this_sequence A047782 A106565 A092166
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000
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