|
%I #5 Mar 30 2012 18:55:29
%S 1,6,1,18,24,1,40,180,60,1,75,800,900,120,1,126,2625,7000,3150,210,1,
%T 196,7056,36750,39200,8820,336,1,288,16464,148176,308700,164640,21168,
%U 504,1,405,34560,493920,1778112,1852200,564480,45360,720,1,550,66825,1425600,8149680,14669424,8731800,1663200,89100,990,1,726,121000,3675375,31363200,89646480,92207808,34303500,4356000,163350,1320,1
%N Triangle a(n,k) = binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2) read by rows.
%C Row sums are 1, 7, 43, 281, 1896, 13112, 92359,...
%e Triangle begins:
%e 1
%e 6,1
%e 18,24,1
%e 40,180,60,1
%e 75,800,900,120,1
%e 126,2625,7000,3150,210,1
%e 196,7056,36750,39200,8820,336,1
%e 288,16464,148176,308700,164640,21168,504,1
%e 405,34560,493920,1778112,1852200,564480,45360,720,1
%p A187552 := proc(n,k) binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2) ; end proc:
%t Table[Binomial[n, k]Binomial[n + 1, k + 1]Binomial[n + 2, k + 2], {n, 0, 8}, {k, 0, 8}]//MatrixForm
%o (Maxima) create_list(binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2),n,0,8,k,0,n);
%Y Cf. A103371, A002411 (column k=0), A165187 (column k=1), A007531 (subdiagonal)
%K nonn,easy,tabl
%O 0,2
%A _Emanuele Munarini_, Mar 11 2011
|
