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%I #5 Dec 21 2016 09:42:50
%S 1,0,0,2,15,-20,-634,2436,42411,-233510,-11619696,49163400,2036481646,
%T -16025646000,-918152531964,5815779836440,409507398512787,
%U -3500207461700030,-252977369776337212,2287457363619598128,206314648049383192746,-2015385286805661512720,-189234286870610655433500,2114103576405833262908120,225453932801460863956791550,-2618254080140270392494246300,-303684082923060566479507972944
%N Central terms of triangles A278886 and A278887: a(n) = A278886(n,n) = A278887(n,n+1) for n>=0.
%C E.g.f. of triangle A278886 is B = B(x,y) where: A^2 + B^2 + C^2 = 1 + y^2 and A^3 + B^3 + C^3 = 1 + y^3, with functions A = A(x,y) and C = C(x,y) described by A278885 and A278887, respectively.
%H Paul D. Hanna, <a href="/A278889/b278889.txt">Table of n, a(n) for n = 0..60</a>
%e E.g.f.: G(x) = 1 + 2*x^3/3! + 15*x^4/4! - 20*x^5/5! - 634*x^6/6! + 2436*x^7/7! + 42411*x^8/8! - 233510*x^9/9! - 11619696*x^10/10! + 49163400*x^11/11! + 2036481646*x^12/12! - 16025646000*x^13/13! - 918152531964*x^14/14! + 5815779836440*x^15/15! +...
%o (PARI) {A278886(n,k) = my(A=x, B=1, C=y); for(i=1, n,
%o A = intformal(B*C^2 - B^2*C +x*O(x^n));
%o B = 1 + intformal(C*A^2 - C^2*A);
%o C = y + intformal(A*B^2 - A^2*B); ); polcoeff( n!*polcoeff(B, n, x), k, y)}
%o for(n=0,20, print1(A278886(n,n),", "))
%o (PARI) {A278887(n,k) = my(A=x, B=1, C=y); for(i=1, n,
%o A = intformal(B*C^2 - B^2*C +x*O(x^n));
%o B = 1 + intformal(C*A^2 - C^2*A);
%o C = y + intformal(A*B^2 - A^2*B); ); polcoeff( n!*polcoeff(C, n, x), k, y)}
%o for(n=0,20, print1(A278887(n,n+1),", "))
%Y Cf. A278885 (A(x,y)), A278886 (B(x,y)), A278887 (C(x,y)), A278888.
%K sign
%O 0,4
%A _Paul D. Hanna_, Dec 20 2016
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