A110851 - OEIS

%I #11 Jul 01 2021 16:06:05

%S 1,2016,635376,74974368,4426165368,151473214816,3284214703056,

%T 47855699958816,488526937079580,3601688791018080,19619725782651120,

%U 80347448443237920,250649105469666120,601557853127198688,1118770292985239888,1620288010530347424,1832624140942590534

%N Weight enumerator of [64,63,2] Reed-Muller code RM(5,6).

%H Georg Fischer, <a href="/A110851/b110851.txt">Table of n, a(n) for n = 0..32</a>

%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

%F a(n) = binomial(64, 2*n). - _Georg Fischer_, Jul 01 2021

%e 4426165368*x^8*y^56 + 1620288010530347424*x^30*y^34 + 47855699958816*x^14*y^50 + 601557853127198688*x^26*y^38 + 80347448443237920*x^22*y^42 + 19619725782651120*x^20*y^44 + 488526937079580*x^16*y^48 + 3601688791018080*x^46*y^18 + 19619725782651120*x^44*y^20 + y^64 + 1832624140942590534*x^32*y^32 + 1118770292985239888*x^36*y^28 + 80347448443237920*x^42*y^22 + 1118770292985239888*x^28*y^36 + 3601688791018080*x^18*y^46 + 2016*x^2*y^62 + 635376*x^60*y^4 + 74974368*x^58*y^6 + 74974368*x^6*y^58 + 635376*x^4*y^60 + 3284214703056*x^12*y^52 + 601557853127198688*x^38*y^26 + 1620288010530347424*x^34*y^30 + 151473214816*x^10*y^54 + 250649105469666120*x^24*y^40 + 3284214703056*x^52*y^12 + 47855699958816*x^50*y^14 + 488526937079580*x^48*y^16 + 250649105469666120*x^40*y^24 + x^64 + 151473214816*x^54*y^10 + 4426165368*x^56*y^8 + 2016*x^62*y^2

%p seq(binomial(64, 2*n), n=0..32); # _Georg Fischer_, Jul 01 2021

%t RecurrenceTable[{(2*n^2-n)*a[n]==(2*n^2-131*n+2145)*a[n-1], a[0]==1}, a[n],{n, 0, 33}] (* _Georg Fischer_, Jul 01 2021 *)

%Y Cf. A110829 (RM(2,3)), A110839 (RM(3,4)), A110847 (RM(4,5)), A110852 (32nd root).

%K nonn,fini,full

%O 0,2

%A _N. J. A. Sloane_ and _Nadia Heninger_ Aug 18 2005