A278888 Central terms of triangle A278885: a(n) = A278885(n,n+1) = -A278885(n,n) for n>=1.

1, 0, -2, 6, 104, 130, -7480, 17808, 790524, -113170, -206401200, 259762932, 53140218296, -111175815660, -24172057073456, 25301079682096, 12946893572092052, -32517981767052650, -8943735216460534192, 16410991703475470220, 7930971475493259708440, -19662403949243519946900, -8179625437444893103218320, 21740998917740950059114560, 10426747097560071845593768504, -28225693942184808133067863860, -15345614872626105712148352012640

Offset

1,3

Comments

E.g.f. of triangle A278885 is A = A(x,y) where: A^2 + B^2 + C^2 = 1 + y^2 and A^3 + B^3 + C^3 = 1 + y^3, with functions B = B(x,y) and C = C(x,y) described by A278886 and A278887, respectively.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..60

Example

E.g.f.: G(x) = x - 2*x^3/3! + 6*x^4/4! + 104*x^5/5! + 130*x^6/6! - 7480*x^7/7! + 17808*x^8/8! + 790524*x^9/9! - 113170*x^10/10! - 206401200*x^11/11! + 259762932*x^12/12! + 53140218296*x^13/13! - 111175815660*x^14/14! - 24172057073456*x^15/15! +...

Prog

(PARI) {A278885(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(A, n, x), k, y)}
for(n=1, 20, print1(A278885(n, n+1), ", "))

Crossrefs

Cf. A278885 (A(x,y)), A278886 (B(x,y)), A278887 (C(x,y)), A278889.

Sequence in context: A123257 A230927 A054247 * A099790 A294906 A284262

Adjacent sequences: A278885 A278886 A278887 * A278889 A278890 A278891

Keyword

sign

Author

Paul D. Hanna, Dec 20 2016

Status

approved