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 A128086 A diagonal of the triangle A128084 of coefficients of q in the q-analog of the even double factorials: a(n) = A128084(n,n). 6
 1, 1, 2, 7, 24, 86, 315, 1170, 4389, 16588, 63064, 240901, 923858, 3554747, 13716315, 53054703, 205651975, 798645126, 3106669575, 12102626404, 47210910670, 184385864445, 720920510115, 2821499709615, 11052719207369, 43333403693711 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See A128082 for a diagonal of the triangle A128080 of coefficients of q in the q-analog of the odd double factorials. LINKS EXAMPLE a(n) is the n-th term in the q-analog of even double factorial (2n)!!, in which the coefficients of q (triangle A128084) begin: (1); 1,(1); 1,2,(2),2,1; 1,3,5,(7),8,8,7,5,3,1; 1,4,9,16,(24),32,39,44,46,44,39,32,24,16,9,4,1; 1,5,14,30,54,(86),125,169,215,259,297,325,340,340,325,297,...; 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-q)), n, q)) CROSSREFS Cf. A000165 ((2n)!!); A128084 (triangle), A128085 (central terms). Sequence in context: A053368 A141753 A014300 * A131824 A256938 A150389 Adjacent sequences:  A128083 A128084 A128085 * A128087 A128088 A128089 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 14 2007 STATUS approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)