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A128082 A diagonal of the triangle A128080 of coefficients of q in the q-analog of the odd double factorials: a(n) = A128080(n+1,n). 5
1, 1, 3, 9, 31, 110, 400, 1477, 5516, 20775, 78762, 300179, 1148995, 4413877, 17007798, 65707390, 254430080, 987162527, 3836843836, 14936223511, 58226118626, 227271470103, 888117198666, 3474154716353, 13603246639501 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1) = A181971(2*n,n). - Reinhard Zumkeller, Jul 09 2012

LINKS

Table of n, a(n) for n=0..24.

EXAMPLE

a(n) is the n-th term in the q-analog of odd double factorial (2n+1)!!,

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

1;

(1);

1,(1),1;

1,2,(3),3,3,2,1;

1,3,6,(9),12,14,15,14,12,9,6,3,1;

1,4,10,19,(31),45,60,74,86,94,97,94,86,74,60,45,31,19,10,4,1;

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

PROG

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

CROSSREFS

Cf. A001147 ((2n-1)!!); A128080 (triangle), A128081 (central terms).

Sequence in context: A148968 A148969 A112566 * A148970 A151459 A151033

Adjacent sequences:  A128079 A128080 A128081 * A128083 A128084 A128085

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 14 2007

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)