login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193762 Triangle read by rows giving coefficients of Genocchi q-numbers B_n(1,q) (n >= 1) expanded in powers of q. 1
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 (list; graph; refs; listen; history; text; internal format)
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-polynĂ´mes 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 18:36 EDT 2021. Contains 348155 sequences. (Running on oeis4.)