This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A159749 The decomposition of a certain labeled universe (A052584), triangle read by rows. 1
 2, 2, 4, 2, 12, 16, 0, 24, 96, 96, -8, 0, 320, 960, 768, 0, -240, 0, 4800, 11520, 7680, 240, 0, -6720, 0, 80640, 161280, 92160, 0, 13440, 0, -188160, 0, 1505280, 2580480, 1290240, -24192, 0, 645120, 0, -5419008, 0, 30965760, 46448640, 20643840 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS T(n,k) is a weighted binomial sum of the Bernoulli numbers A027641/A027642 with A027641(1) = 1, which amounts to the definition B_{n} = B_{n}(1). LINKS FORMULA T(n,k) = (n+1)!*C(n,k)*B_{n-k}*2^(k+1)/(k+1). T(n,n) = A066318(n+1) = n!*2^(n+1) (necklaces with n labeled beads of 2 colors; see also A032184). Sum_{k=0..n} T(n,k) = A052584(n+1) = (n+1)!*(1+2^n). EXAMPLE 2 2, 4 2, 12, 16 0, 24, 96, 96 -8, 0, 320, 960, 768 0, -240, 0, 4800, 11520, 7680 240, 0, -6720, 0, 80640, 161280, 92160 MAPLE T := (n, k) -> (n+1)!*binomial(n, k)*bernoulli(n-k, 1)*2^(k+1)/(k+1); MATHEMATICA T[n_, k_] := (n+1)! Binomial[n, k] BernoulliB[n-k, 1] 2^(k+1)/(k+1); Table[T[n, k], {n, 0, 8}, {k, 0, n}] (* Jean-François Alcover, Jun 17 2019 *) CROSSREFS Cf. A027641, A027642, A052584. Sequence in context: A059427 A137777 A126984 * A227293 A102416 A227509 Adjacent sequences:  A159746 A159747 A159748 * A159750 A159751 A159752 KEYWORD sign,tabl AUTHOR Peter Luschny, Apr 20 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)