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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
OFFSET
1,2
COMMENTS
Row lengths are 1, 2, 4, 7, 11, 16, 22, 29, ...
LINKS
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Aug 04 2011
STATUS
approved