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 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}. 9
 1, 1, 7, 62, 657, 7636, 93846, 1199892, 15796439, 212681976, 2915017360, 40536016030, 570497115729, 8110661588734, 116307527411482, 1680341334827514, 24435006625667338, 357366669614512168, 5253165510907071170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 0..835 (terms < 10^1000, first 251 terms from Alois P. Heinz) Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author] L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991), 315-324. FORMULA 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. For 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, Sep 24 2006 EXAMPLE 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}. MAPLE b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;       `if`(n>m, 0, `if`(n=m, 1, b(abs(n-i), i-1) +b(n+i, i-1)))     end: a:= n-> b(4*n, 4*n-1): seq(a(n), n=0..30);  # Alois P. Heinz, Oct 30 2011 MATHEMATICA b[n_, i_] := b[n, i] = Module[{m = i*(i+1)/2}, If[n > m, 0, If[n == m, 1, b[Abs[n-i], i-1] + b[n+i, i-1]]]]; a[n_] := b[4*n, 4*n-1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Sep 26 2013, translated from Alois P. Heinz's Maple program *) CROSSREFS Cf. A060468, A007219, A107350, a(n)=A058377(4n), A227850. Sequence in context: A327588 A287481 A289212 * A055066 A216534 A167550 Adjacent sequences:  A060002 A060003 A060004 * A060006 A060007 A060008 KEYWORD nonn AUTHOR Roland Bacher, Mar 15 2001 EXTENSIONS More terms from Alois P. Heinz, Oct 30 2011 STATUS approved

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Last modified January 18 00:48 EST 2022. Contains 350410 sequences. (Running on oeis4.)