

A082134


E.g.f. x*exp(3*x)*cosh(x).


7



0, 1, 6, 30, 144, 680, 3168, 14560, 66048, 296064, 1313280, 5772800, 25178112, 109078528, 469819392, 2013388800, 8590196736, 36507779072, 154620002304, 652837519360, 2748784312320, 11544883101696, 48378534690816
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OFFSET

0,3


COMMENTS

Binomial transform of A082133. 3rd binomial transform of (0,1,0,3,0,5,0,7,....)
Let P(A) be the power set of an nelement set A and B be the Cartesian product of P(A) with itself. Then remove (y,x) from B when (x,y) is in B and x <> y and call this R35. Then a(n) = the sum of the size of the intersection of x and y for every (x,y) of R35..  Ross La Haye, Dec 30 2007; edited Jan 05 2013
A133224 is the analogous sequence if "Intersection" is replaced by "Union" and A002697 is the analogous sequence if "Intersection" is replaced by "Symmetric difference". Here, X Intersection Y = Y Intersection X is considered as the same set [Relation (37): T_Q(n) in document of Ross La Haye in reference]. If we want to consider that X Intersection Y and Y Intersection X are two distinct formula for describing the same set, see A002697. [Bernard Schott, Jan 19 2013]


REFERENCES

Ross La Haye, Binary Relations on the Power Set of an nElement Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.


LINKS

Table of n, a(n) for n=0..22.
Index to sequences with linear recurrences with constant coefficients, signature (12,52,96,64).


FORMULA

a(n) = n*(2^(n1)+4^(n1))/2.
E.g.f.: x*exp(3*x)*cosh(x).
Conjecture: (n+28)*a(n) +(n282)*a(n1) +2*(17*n+423)*a(n2) +8*(7*n94)*a(n3)=0.  R. J. Mathar, Nov 29 2012
G.f.: x*(10*x^26*x+1) / ((2*x1)^2*(4*x1)^2). [Colin Barker, Dec 10 2012]


PROG

(PARI) a(n)=n*(2^n+4^n)/2 \\ Charles R Greathouse IV, Jan 14 2013


CROSSREFS

Cf. A057711, A082135.
Cf. A133224, A002697.
Sequence in context: A026749 A003279 A221397 * A030192 A026376 A026899
Adjacent sequences: A082131 A082132 A082133 * A082135 A082136 A082137


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Apr 06 2003


STATUS

approved



