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 A202039 Triangle T(n,m) = coefficient of x^n in expansion of (1/2-1/2*(1-8*x)^1/4)^m = sum(n>=m, T(n,m) x^n), n>=1, m>=1. 0

%I

%S 1,3,1,14,6,1,77,37,9,1,462,238,69,12,1,2926,1582,510,110,15,1,19228,

%T 10780,3738,920,160,18,1,129789,74877,27405,7389,1495,219,21,1,894102,

%U 528022,201569,58156,13075,2262,287,24,1,6258714,3769370,1488762,452826,110143,21417,3248,364,27,1

%N Triangle T(n,m) = coefficient of x^n in expansion of (1/2-1/2*(1-8*x)^1/4)^m = sum(n>=m, T(n,m) x^n), n>=1, m>=1.

%F T(n,m) = (m*sum(k=0..n-m, (-1)^(n-m-k)*binomial(n+k-1,n-1)*sum(j=0..k, binomial(j,n-m+(-3)*k+2*j)*binomial(k,j)*2^(2*n-2*m+(-5)*k+3*j)*3^(-n+m+3*k-j))))/n.

%F T(n,m) = (m*sum(k=m..n,binomial(-m+2*k-1,k-1)*2^(n-k)*binomial(2*n-k-1,n-1)))/n. - _Vladimir Kruchinin_, Dec 21 2011

%F T(n,m) = (m/n)*2^(n-m)*binomial(2*n-m-1,n-m)*hypergeometric([1/2+m/2,m/2,m-n],[m,1+m-2*n],2) for n>1, m>1. - _Peter Luschny_, Jan 04 2012

%e 1,

%e 3, 1,

%e 14, 6, 1,

%e 77, 37, 9, 1,

%e 462, 238, 69, 12, 1,

%e 2926, 1582, 510, 110, 15, 1

%o (Maxima)

%o T(n,m):=(m*sum((-1)^(n-m-k)*binomial(n+k-1,n-1)*sum(binomial(j,n-m+(-3)*k+2*j)*binomial(k,j)*2^(2*n-2*m+(-5)*k+3*j)*3^(-n+m+3*k-j),j,0,k),k,0,n-m))/n;

%o T(n,m):=(m*sum(binomial(-m+2*k-1,k-1)*2^(n-k)*binomial(2*n-k-1,n-1),k,m,n))/n;

%K nonn,tabl

%O 1,2

%A _Vladimir Kruchinin_, Dec 10 2011

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Last modified February 5 22:19 EST 2023. Contains 360087 sequences. (Running on oeis4.)