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 A278889 Central terms of triangles A278886 and A278887: a(n) = A278886(n,n) = A278887(n,n+1) for n>=0. 4
 1, 0, 0, 2, 15, -20, -634, 2436, 42411, -233510, -11619696, 49163400, 2036481646, -16025646000, -918152531964, 5815779836440, 409507398512787, -3500207461700030, -252977369776337212, 2287457363619598128, 206314648049383192746, -2015385286805661512720, -189234286870610655433500, 2114103576405833262908120, 225453932801460863956791550, -2618254080140270392494246300, -303684082923060566479507972944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS Paul D. Hanna, Table of n, a(n) for n = 0..60 EXAMPLE 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! +... PROG (PARI) {A278886(n, k) = my(A=x, B=1, C=y); for(i=1, n, A = intformal(B*C^2 - B^2*C +x*O(x^n)); B = 1 + intformal(C*A^2 - C^2*A); C = y + intformal(A*B^2 - A^2*B); ); polcoeff( n!*polcoeff(B, n, x), k, y)} for(n=0, 20, print1(A278886(n, n), ", ")) (PARI) {A278887(n, k) = my(A=x, B=1, C=y); for(i=1, n, A = intformal(B*C^2 - B^2*C +x*O(x^n)); B = 1 + intformal(C*A^2 - C^2*A); C = y + intformal(A*B^2 - A^2*B); ); polcoeff( n!*polcoeff(C, n, x), k, y)} for(n=0, 20, print1(A278887(n, n+1), ", ")) CROSSREFS Cf. A278885 (A(x,y)), A278886 (B(x,y)), A278887 (C(x,y)), A278888. Sequence in context: A244324 A143660 A198391 * A075722 A169597 A280288 Adjacent sequences: A278886 A278887 A278888 * A278890 A278891 A278892 KEYWORD sign AUTHOR Paul D. Hanna, Dec 20 2016 STATUS approved

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Last modified June 2 10:25 EDT 2023. Contains 363097 sequences. (Running on oeis4.)