A038224 - OEIS

%I #10 Feb 22 2020 20:26:35

%S 1,3,6,9,36,36,27,162,324,216,81,648,1944,2592,1296,243,2430,9720,

%T 19440,19440,7776,729,8748,43740,116640,174960,139968,46656,2187,

%U 30618,183708,612360,1224720,1469664,979776,279936,6561,104976

%N Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*6^j.

%D B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.

%e 1;

%e 3,6;

%e 9,36,36;

%e 27,162,324,216;

%e 81,648,1944,2592,1296;

%e 243,2430,9720,19440,19440,7776;

%e 729,8748,43740,116640,174960,139968,46656;

%e 2187,30618,183708,612360,1224720,1469664,979776,279936;

%p A038224 := proc(n,k)

%p         if k < 0 or k > n then

%p                 0;

%p         else

%p                 binomial(n,k)*3^(n-k)*6^k ;

%p         end if;

%p end proc: # _R. J. Mathar_, Mar 26 2013

%t Table[Binomial[i,j]3^(i-j) 6^j,{i,0,10},{j,0,i}]//Flatten (* _Harvey P. Dale_, Feb 22 2020 *)

%K nonn,tabl,easy

%O 0,2

%A _N. J. A. Sloane_.