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A176390 A symmetrical triangle:t(n,m)=1 - (1 + n)^(n + 1)* (1 - 1/(n + 1))^(n + 1) + (n + 1)^(n + 2)*Binomial[n, m]((m + 1)/(n + 1))^(m + 1)*(1 - ( m + 1)/(n + 1))^(n - m + 1) 0

%I #2 Mar 30 2012 17:34:40

%S 1,1,1,1,16,1,1,273,273,1,1,4856,6246,4856,1,1,95065,134785,134785,

%T 95065,1,1,2073408,3094575,3410240,3094575,2073408,1,1,50255905,

%U 77413889,89782273,89782273,77413889,50255905,1,1,1345053808,2116602172

%N A symmetrical triangle:t(n,m)=1 - (1 + n)^(n + 1)* (1 - 1/(n + 1))^(n + 1) + (n + 1)^(n + 2)*Binomial[n, m]((m + 1)/(n + 1))^(m + 1)*(1 - ( m + 1)/(n + 1))^(n - m + 1)

%C The sequence is an adjusted probability based symmetrical triangle.

%C Row sums are:

%C {1, 2, 18, 548, 15960, 459702, 13746208, 434904136, 14654790000, 526697204570,...}.

%F t(n,m)=1 - (1 + n)^(n + 1)* (1 - 1/(n + 1))^(n + 1) + (n + 1)^(n + 2)*Binomial[n, m]((m + 1)/(n + 1))^(m + 1)*(1 - ( m + 1)/(n + 1))^(n - m + 1)

%e {1},

%e {1, 1},

%e {1, 16, 1},

%e {1, 273, 273, 1},

%e {1, 4856, 6246, 4856, 1},

%e {1, 95065, 134785, 134785, 95065, 1},

%e {1, 2073408, 3094575, 3410240, 3094575, 2073408, 1},

%e {1, 50255905, 77413889, 89782273, 89782273, 77413889, 50255905, 1},

%e {1, 1345053808, 2116602172, 2532959344, 2665559350, 2532959344, 2116602172, 1345053808, 1},

%e {1, 39471376041, 63074539521, 77094686721, 83708000001, 83708000001, 77094686721, 63074539521, 39471376041, 1}

%t t[n_, m_] = 1 - (1 + n)^(n + 1)* (1 - 1/(n + 1))^(n + 1) + (n + 1)^(n + 2)*Binomial[n, m]((m + 1)/(n + 1))^(m + 1)*(1 - (m + 1)/(n + 1))^(n - m + 1);

%t Table[Table[t[n, m], {m, 0, n - 1}], {n, 1, 10}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 16 2010

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Last modified April 12 16:59 EDT 2024. Contains 371635 sequences. (Running on oeis4.)