A326795 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A326795

E.g.f. B(x) = B(x,x), where B(x,y) is the e.g.f. of triangle A326798.

1, -1, 1, 119, -671, -118801, 1578721, 472546983, -11434861759, -5281001286433, 202651641610561, 134214161576815319, -7489030360212947039, -6743315366908570697521, 515685193530081985152289, 606502419281376583942534919, -60891202949811176406832459647, -90683512562992732210541162641985, 11568533431831545319762169579235457, 21284623320002783970199662076124812599

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Equals the row sums of triangle A326798.

LINKS

Table of n, a(n) for n=0..19.

FORMULA

E.g.f. B(x) and related functions A(x) and C(x), defined by A326794 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.: B(x) = 1 - x^2/2! + x^4/4! + 119*x^6/6! - 671*x^8/8! - 118801*x^10/10! + 1578721*x^12/12! + 472546983*x^14/14! - 11434861759*x^16/16! - 5281001286433*x^18/18! + 202651641610561*x^20/20! + ....

PROG

(PARI) {a(n) = 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, (2*n)! * polcoeff( polcoeff(Bx, 2*n-2*k, x), 2*k, y))}

for(n=0, 20, print1( a(n), ", "))