A193762 Triangle read by rows giving coefficients of Genocchi q-numbers B_n(1,q) (n >= 1) expanded in powers of q.

1, 2, 1, 5, 7, 4, 1, 14, 36, 45, 35, 18, 6, 1, 42, 165, 330, 440, 433, 330, 198, 93, 33, 8, 1, 132, 715, 2002, 3822, 5551, 6496, 6331, 5239, 3718, 2268, 1183, 520, 187, 52, 10, 1, 429, 3003, 10920, 27300, 52500, 82476, 109800, 126885, 129360, 117635, 96096, 70800, 47100, 28245, 15195, 7269, 3048, 1095, 325, 75, 12, 1, 1430, 12376, 55692

Offset

1,2

Comments

Row lengths are 1, 2, 4, 7, 11, 16, 22, 29, ...

Links

Table of n, a(n) for n=1..66.

Han, Guo-Niu; and Zeng, Jiang; q-polynômes de Gandhi et statistique de Denert, Discrete Math. 205 (1999), 119-143. See p. 140.

Example

   1
   2 +    q
   5 +  7*q +  4*q^2 +    q^3
  14 + 36*q + 45*q^2 + 35*q^3 + 18*q^4 + 6*q^5 + q^6
  ...

Maple

qBrack := proc(n, q)
        add(q^i, i=0..n-1) ;
end proc:
B := proc(n, x, q)
        a :=0 ;
        for npr from 1 to n do
                q^(npr-1)*(1+q*x-x)*t^npr*mul((qBrack(k, q)+q^k*x)^2, k=1..npr-1) ;
                %/mul(q^(k-1)*(1+q*x-x)+t*(qBrack(k-1, q)+q^(k-1)*x)^2, k=1..npr) ;
                a := a+coeftayl(%, t=0, n) ;
        end do;
        expand(a) ;
end proc:
A193762_row := proc(n)
        B(n, 1, q) ;
end proc:
A193762 := proc(n, k)
        coeftayl( A193762_row(n), q=0, k) ;
end proc: # R. J. Mathar, Oct 02 2011

Crossrefs

Sequence in context: A293845 A249265 A259972 * A268489 A198422 A105459

Adjacent sequences: A193759 A193760 A193761 * A193763 A193764 A193765

Keyword

nonn,tabf

Author

N. J. A. Sloane, Aug 04 2011

Status

approved