|
| |
|
|
A002050
|
|
Number of simplices in barycentric subdivision of n-simplex.
(Formerly M3939 N1622)
|
|
8
| |
|
|
0, 1, 5, 25, 149, 1081, 9365, 94585, 1091669, 14174521, 204495125, 3245265145, 56183135189, 1053716696761, 21282685940885, 460566381955705, 10631309363962709, 260741534058271801, 6771069326513690645
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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]
|
|
|
REFERENCES
| Ulrike Sattler, Decidable classes of formal power series with nice closure properties, Diplomarbeit im Fach Informatik, Univ. Erlangen - Nuernberg, Jul 27 1994
G. J. Simmons, A combinatorial problem associated with a family of combination locks, Math. Mag., 37 (1964), 127-132 (but there are errors).
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).
J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 149
|
|
|
FORMULA
| 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]
|
|
|
MATHEMATICA
| 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]
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, n!*polcoeff(subst((y+y^2)/(1-y), y, exp(x+x*O(x^n))-1), n))
|
|
|
CROSSREFS
| a(n) = A000629(n) - 1.
Sequence in context: A121639 A098349 A098212 * A047782 A106565 A200031
Adjacent sequences: A002047 A002048 A002049 * A002051 A002052 A002053
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000
|
| |
|
|
