The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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: A132437 A331610 A331618 * A186264 A140286 A199416 Adjacent sequences:  A128078 A128079 A128080 * A128082 A128083 A128084 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 14 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 04:35 EDT 2020. Contains 337295 sequences. (Running on oeis4.)