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A128592 Triangle, read by rows, of coefficients of q^(nk+k) in the q-analog of the odd double factorials: T(n,k) = [q^(nk+k)] Product_{j=1..n+1} (1-q^(2j-1))/(1-q) for n>0, with T(0,0)=1. 4
1, 1, 1, 1, 3, 1, 1, 12, 12, 1, 1, 45, 97, 45, 1, 1, 170, 696, 696, 170, 1, 1, 644, 4784, 8447, 4784, 644, 1, 1, 2451, 32230, 92003, 92003, 32230, 2451, 1, 1, 9365, 214978, 946330, 1487477, 946330, 214978, 9365, 1, 1, 35908, 1426566, 9417798, 21856230, 21856230 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..50.

FORMULA

T(n,k) = A128080(n+1,nk+k) where A128080 is the triangle of coefficients of q in the q-analog of the odd double factorials.

EXAMPLE

Triangle begins:

1;

1, 1;

1, 3, 1;

1, 12, 12, 1;

1, 45, 97, 45, 1;

1, 170, 696, 696, 170, 1;

1, 644, 4784, 8447, 4784, 644, 1;

1, 2451, 32230, 92003, 92003, 32230, 2451, 1;

1, 9365, 214978, 946330, 1487477, 946330, 214978, 9365, 1;

1, 35908, 1426566, 9417798, 21856230, 21856230, 9417798, 1426566, 35908, 1;

1, 138104, 9441417, 91852376, 302951392, 441170745, 302951392, 91852376, 9441417, 138104, 1;

PROG

(PARI) T(n, k)=if(k<0 || k>n*(n+1), 0, if(n==0, 1, polcoeff(prod(j=1, n+1, (1-q^(2*j-1))/(1-q)), (n+1)*k, q)))

CROSSREFS

Cf. A128080; A001147 ((2n-1)!!); A128593 (column 1), A128594 (column 2), A128595 (row sums); variant: A128596.

Sequence in context: A134523 A098778 A078122 * A156584 A209424 A129619

Adjacent sequences:  A128589 A128590 A128591 * A128593 A128594 A128595

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Mar 12 2007

STATUS

approved

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)