

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
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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

Table of n, a(n) for n=0..44.


FORMULA

T(n,k) = (n+1)!*C(n,k)*B_{nk}*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(nk, 1)*2^(k+1)/(k+1);


MATHEMATICA

T[n_, k_] := (n+1)! Binomial[n, k] BernoulliB[nk, 1] 2^(k+1)/(k+1);
Table[T[n, k], {n, 0, 8}, {k, 0, n}] (* JeanFrançois 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



