A326794 E.g.f. A(x) = A(x,x), where A(x,y) is the e.g.f. of triangle A326797.

1, -4, -24, 832, 14080, -1178112, -40198144, 6102368256, 350164353024, -84145181818880, -7290125908443136, 2544780720155394048, 310189596697035800576, -148294858002251055628288, -24194060487469916561080320, 15177404660097357616248782848, 3193403421862605489912894455808, -2544493850062379218318289711136768, -670888183682611536585868983069048832, 661838176807194100001000065515567185920

Offset

1,2

Comments

Equals the row sums of triangle A326797.

Links

Table of n, a(n) for n=1..20.

Formula

E.g.f. A(x) and related functions B(x) and C(x), defined by A326795 and A326796, 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.: A(x) = x - 4*x^3/3! - 24*x^5/5! + 832*x^7/7! + 14080*x^9/9! - 1178112*x^11/11! - 40198144*x^13/13! + 6102368256*x^15/15! + 350164353024*x^17/17! - 84145181818880*x^19/19! + ...

Prog

(PARI) {a(n) = my(Ax=1, Bx=x, Cx=1, Ay=1, 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+1)! * polcoeff( polcoeff(Ax, 2*n-2*k+1, x), 2*k, y))}
for(n=0, 20, print1( a(n), ", "))

Crossrefs

Cf. A326795, A326796, A326797.

Sequence in context: A347480 A058171 A196866 * A223005 A009043 A024251

Adjacent sequences: A326791 A326792 A326793 * A326795 A326796 A326797

Keyword

sign

Author

Paul D. Hanna, Aug 05 2019

Status

approved