A128595 Row sums of triangle A128592.

1, 2, 5, 26, 189, 1734, 19305, 253370, 3828825, 65473006, 1249937325, 26352843470, 608142583125, 15247003381854, 412685556908625, 11993673995924378, 372509404162520625, 12313505304343363126, 431620764875678503125

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

Table of n, a(n) for n=0..18.

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}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 27 2024 *)

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

Cf. A128592; A128080; A001147 ((2n-1)!!); A128593 (column 1), A128594 (column 2).

Sequence in context: A334639 A072268 A019014 * A358715 A180749 A323299

Adjacent sequences: A128592 A128593 A128594 * A128596 A128597 A128598

Keyword

nonn

Author

Paul D. Hanna, Mar 12 2007

Status

approved