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A128081 Central coefficients of q in the q-analog of the odd double factorials: a(n) = [q^(n(n-1)/2)] Product_{j=1..n} (1-q^(2j-1))/(1-q). 4
1, 1, 1, 3, 15, 97, 815, 8447, 104099, 1487477, 24188525, 441170745, 8920418105, 198066401671, 4791181863221, 125421804399845, 3532750812110925, 106538929613501939, 3425126166609830467, 116938867144129019137 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..19.

EXAMPLE

a(n) is the central term of the q-analog of odd double factorials,

in which the coefficients of q (triangle A128080) begin:

n=0: (1);

n=1: (1);

n=2: 1,(1),1;

n=3: 1,2,3,(3),3,2,1;

n=4: 1,3,6,9,12,14,(15),14,12,9,6,3,1;

n=5: 1,4,10,19,31,45,60,74,86,94,(97),94,86,74,60,45,31,19,10,4,1;

n=6: 1,5,15,34,65,110,170,244,330,424,521,614,696,760,801,(815),...;

The terms enclosed in parenthesis are initial terms of this sequence.

PROG

(PARI) a(n)=if(n==0, 1, polcoeff(prod(k=1, n, (1-q^(2*k-1))/(1-q)), n*(n-1)/2, q))

CROSSREFS

Cf. A001147 ((2n-1)!!); A128080 (triangle), A128082 (diagonal).

Sequence in context: A060148 A143435 A132437 * A186264 A140286 A199416

Adjacent sequences:  A128078 A128079 A128080 * A128082 A128083 A128084

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 14 2007

STATUS

approved

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Last modified April 23 03:26 EDT 2019. Contains 322380 sequences. (Running on oeis4.)