

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]


LINKS

Table of n, a(n) for n=0..22.
Ross La Haye, Binary Relations on the Power Set of an nElement Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
Index entries for 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]


MATHEMATICA

Table[n (2^(n  1) + 4^(n  1))/2, {n, 0, 22}] (* Michael De Vlieger, Nov 29 2015 *)


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



