# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a292476 Showing 1-1 of 1 %I A292476 #20 Mar 10 2023 05:39:19 %S A292476 1,0,2,2,8,20,68,206,692,2306,7930,27492,96792,343670,1231932,4447510, %T A292476 16164914,59086618,217091832,801247614,2969432270,11045446688, %U A292476 41224168020,154329373022,579377940390,2180684278698,8227240466520,31107755899600 %N A292476 Number of solutions to +-1 +- 3 +- 5 +- 7 +- ... +- (4*n-1) = 0. %F A292476 Constant term in the expansion of Product_{k=1..2*n} (x^(2*k-1)+1/x^(2*k-1)). %F A292476 a(n) = 2*A156700(n) for n > 0. %e A292476 For n=2 the 2 solutions are +1-3-5+7 = 0 and -1+3+5-7 = 0. %e A292476 For n=3 the 2 solutions are +1+3+5-7+9-11 = 0 and -1-3-5+7-9+11 = 0. %t A292476 a[n_] := SeriesCoefficient[Product[x^(2k - 1) + 1/x^(2k - 1), {k, 1, 2n}], {x, 0, 0}]; %t A292476 Table[a[n], {n, 0, 27}] (* _Jean-François Alcover_, Mar 10 2023 *) %o A292476 (PARI) {a(n) = polcoeff(prod(k=1, 2*n, x^(2*k-1)+1/x^(2*k-1)), 0)} %Y A292476 Cf. A063865, A156700, A292496. %K A292476 nonn %O A292476 0,3 %A A292476 _Seiichi Manyama_, Sep 17 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE