Search: id:A060005 Results 1-1 of 1 results found. %I A060005 %S A060005 1,1,7,62,657,7636,93846,1199892,15796439,212681976,2915017360, %T A060005 40536016030,570497115729,8110661588734,116307527411482, %U A060005 1680341334827514,24435006625667338,357366669614512168 %N A060005 Number of ways of partitioning the integers {1,2,..,4n} into two (unordered) sets such that the sums of parts are equal in both sets (parts in either set will add up to (4n)*(4n+1)/4). Number of solutions to {1 +- 2 +- 3 +- ... +- 4n=0}. %D A060005 L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991), 315-324. %H A060005 S. R. Finch, Signum equations and extremal coefficients. %F A060005 a(0)=1 and a(n) is half the coefficient of q^0 in product('(q^(-k)+q^k)', 'k'=1..4*n) for n >= 1. %F A060005 n>=1, a(n)=(1/Pi)*16^n*J(4n) where J(n)=integral(t=0,Pi/2,cos(t)cos(2t)...cos(nt)dt) - Benoit Cloitre (abmt(AT)orange.fr), Sep 24 2006 %e A060005 a(1)=1 since there is only one way of partitioning {1,2,3,4} into two sets of equal sum, namely {1,4}, {2,3}. %Y A060005 Cf. A060468, A007219, A107350, a(n)=A058377(4n) %Y A060005 Sequence in context: A145507 A047685 A024089 this_sequence A055066 A167550 A161201 %Y A060005 Adjacent sequences: A060002 A060003 A060004 this_sequence A060006 A060007 A060008 %K A060005 nonn %O A060005 0,3 %A A060005 Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Mar 15 2001 Search completed in 0.002 seconds