A326796 E.g.f. C(x) = C(x,x), where C(x,y) is the e.g.f. of triangle A326799.

2, -4, -154, 1336, 139402, -2516812, -531298962, 16291452784, 5792759106578, -269619415772564, -144868583759257994, 9514326895639572136, 7196653593954009006746, -633707576374342516652764, -641861736344903371972973954, 72970336686693711886017561312, 95350631737851404765088770262050, -13593601759174079774108596113815332, -22265118012504823914985759717325911674

Offset

2,1

Comments

Equals the row sums of triangle A326799.

Links

Table of n, a(n) for n=2..20.

Formula

E.g.f. C(x) and related functions A(x) and B(x), defined by A326794 and A326795, respectively, satisfy:

(1) A(x)^2 + B(x)^2 + C(x)^2 = 1,

(2) A(x)*A'(x) + B(x)*B'(x) + C(x)*C'(x) = 0.

Example

E.g.f.: C(x) = 2*x^2/2! - 4*x^4/4! - 154*x^6/6! + 1336*x^8/8! + 139402*x^10/10! - 2516812*x^12/12! - 531298962*x^14/14! + 16291452784*x^16/16! + 5792759106578*x^18/18! - 269619415772564*x^20/20! + ...

Prog

(PARI) {a(n, k) = my(Ax=x, Bx=1, Cx=x, Ay=y, By=y, Cy=1);
for(i=0, 2*n+1,
Ax = 0 + intformal( Bx*Cy - Cx*By, x) + O(x^(2*n+2));
Bx = 1 + intformal( Cx*Ay - Ax*Cy, x) + O(x^(2*n+2));
Cx = 0 + intformal( Ax*By - Bx*Ay, x) + O(x^(2*n+2));
Ay = 0 + intformal( By*Cx - Cy*Bx, y) + O(y^(2*n+2));
By = 0 + intformal( Cy*Ax - Ay*Cx, y) + O(y^(2*n+2));
Cy = 1 + intformal( Ay*Bx - By*Ax, y) + O(y^(2*n+2));
);
sum(k=0, n, (2*n+2)! * polcoeff( polcoeff(Cx, 2*n-2*k+1, x), 2*k+1, y))}
for(n=0, 20, print1( a(n), ", "))

Crossrefs

Cf. A326794, A326795, A326799.

Sequence in context: A018539 A018544 A192063 * A018558 A296463 A132528

Adjacent sequences: A326793 A326794 A326795 * A326797 A326798 A326799

Keyword

sign

Author

Paul D. Hanna, Aug 05 2019

Status

approved