A202550 - OEIS

%I #12 Aug 09 2015 01:04:23

%S 1,4,1,21,8,1,124,58,12,1,782,416,111,16,1,5144,2997,940,180,20,1,

%T 34845,21752,7653,1760,265,24,1,241196,159062,61068,16014,2940,366,28,

%U 1,1697498,1171136,481944,139712,29600,4544

%N Triangle T(n,m) = coefficient of x^n in the Taylor expansion of [(1-(1-8*x)^(1/4))/(1+(1-8*x)^(1/4))]^m.

%F n*T(n,m) = sum_{i=m..n} i*binomial(i-1,m-1)* sum_{k=0..n-i} (-1)^(n-k-i)*binomial(n+k-1,n-1) *sum_{j=0..k} binomial(j,n-3*k+2*j-i)*binomial(k,j) *2^(2*n-5*k+3*j-2*i) *3^(-n+3*k-j+i).

%e The coefficients start in row n=1 with 1<=m<=n as:

%e 1,

%e 4, 1,

%e 21, 8, 1,

%e 124, 58, 12, 1,

%e 782, 416, 111, 16, 1,

%e 5144, 2997, 940, 180, 20, 1,

%e 34845, 21752, 7653, 1760, 265, 24, 1

%p A202550 := proc(n,m)

%p         (1-(1-8*x)^(1/4)) /(1+(1-8*x)^(1/4)) ;

%p         coeftayl(%^m,x=0,n) ;

%p end proc: # _R. J. Mathar_, Dec 22 2011

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

%Y Cf. A101478.

%K nonn,tabl

%O 1,2

%A _Vladimir Kruchinin_, Dec 20 2011