|
|
A128595
|
|
Row sums of triangle A128592.
|
|
3
|
|
|
1, 2, 5, 26, 189, 1734, 19305, 253370, 3828825, 65473006, 1249937325, 26352843470, 608142583125, 15247003381854, 412685556908625, 11993673995924378, 372509404162520625, 12313505304343363126, 431620764875678503125
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
A128592(n,k) is the coefficient of q^(nk+k) in the q-analog of the odd double factorials (2n-1)!!.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} { [q^(nk+k)] Product_{j=1..n+1} (1-q^(2j-1))/(1-q) } for n>=0.
|
|
MATHEMATICA
|
a[n_] := Sum[SeriesCoefficient[Product[(1-q^(2j-1))/(1-q), {j, 1, n+1}], {q, 0, k(n+1)}], {k, 0, n}];
|
|
PROG
|
(PARI) {a(n)=sum(k=0, n, polcoeff(prod(j=1, n+1, (1-q^(2*j-1))/(1-q)), (n+1)*k, q))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|