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%I #2 Mar 30 2012 17:34:40
%S 1,1,1,1,2,1,1,9,9,1,1,67,117,67,1,1,625,1741,1741,625,1,1,6841,30529,
%T 49501,30529,6841,1,1,86401,635041,1695745,1695745,635041,86401,1,1,
%U 1244881,15504481,69911281,115612993,69911281,15504481,1244881,1,1
%N A symmetrical triangle sequence;q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=1 - n! + n!*c(n, q)/(c[m, q)*c(n - m, q))/Binomial[n, m]
%C Row sums are:
%C {1, 2, 4, 20, 253, 4734, 124243, 4834376, 288934281, 26786718730,
%C 3842906762891,...}.
%F q=2;
%F c(n,q)=Product[1 - q^i, {i, 1, n}];
%F t(n,m,q)=1 - n! + n!*c(n, q)/(c[m, q)*c(n - m, q))/Binomial[n, m]
%e {1},
%e {1, 1},
%e {1, 2, 1},
%e {1, 9, 9, 1},
%e {1, 67, 117, 67, 1},
%e {1, 625, 1741, 1741, 625, 1},
%e {1, 6841, 30529, 49501, 30529, 6841, 1},
%e {1, 86401, 635041, 1695745, 1695745, 635041, 86401, 1},
%e {1, 1244881, 15504481, 69911281, 115612993, 69911281, 15504481, 1244881, 1},
%e {1, 20240641, 437461921, 3403948321, 9531708481, 9531708481, 3403948321, 437461921, 20240641, 1},
%e {1, 367597441, 14047971841, 191951272801, 928692466561, 1572788145601, 928692466561, 191951272801, 14047971841, 367597441, 1}
%t c[n_, q_] = Product[1 - q^i, {i, 1, n}];
%t t[n_, m_, q_] = 1 - n! + n!*c[n, q]/(c[m, q]*c[n - m, q])/Binomial[n,m];
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Apr 17 2010
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