A291821 Central terms of triangle A291820.

1, 2, 38, 1245, 55566, 3062271, 197983540, 14567100211, 1196032764639, 108105913233804, 10651377348228706, 1135394214204504346, 130161542660895451934, 15969338705916554563833, 2088140238440781625249392, 289961586742613652475061397, 42623636996226195002733858964, 6613842247421357561153219091827, 1080515428870235624428208631160409, 185421585676394321869412169323524031

Offset: 1

Author

Paul D. Hanna, Sep 01 2017

Keywords

• nonn

Comments

The g.f. F(x,y) of A291820 satisfies: F(x - x*y*F(x,y), y) = x + x*(1-y)*F(x,y).

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A291820.

Programs

PARI

/* As central terms of triangle A291820 */
{A291820(n, k) = my(A=x); for(i=1, n, A = x + subst(x*A, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A, n, x), k, y)}
for(n=1, 20, print1(A291820(2*n-1, n-1), ", "));

Formula

a(n) = A291820(2*n-1, n-1) for n>=1.