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Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j.
1

%I #15 Apr 22 2014 03:04:43

%S 1,7,5,49,70,25,343,735,525,125,2401,6860,7350,3500,625,16807,60025,

%T 85750,61250,21875,3125,117649,504210,900375,857500,459375,131250,

%U 15625,823543,4117715,8823675,10504375,7503125,3215625,765625,78125

%N Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^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.

%H Vincenzo Librandi, <a href="/A038271/b038271.txt">Rows n = 0..100, flattened</a>

%H Gábor Kallós, <a href="http://dx.doi.org/10.5802/ambp.211">A generalization of Pascal’s triangle using powers of base numbers</a>, Annales mathématiques Blaise Pascal, 13 no. 1 (2006), p. 1-15.

%e Triangle begins:

%e 1,

%e 7, 5,

%e 49, 70, 25,

%e 343, 735, 525, 125,

%e 2401, 6860, 7350, 3500, 625,

%e 16807, 60025, 85750, 61250, 21875, 3125,

%e 117649, 504210, 900375, 857500, 459375, 131250, 15625;

%e ... - _Vincenzo Librandi_, Apr 22 2014

%t Flatten[Table[Binomial[i,j]7^(i-j) 5^j,{i,0,10},{j,0,i}]] (* _Harvey P. Dale_, Apr 20 2014 *)

%K nonn,tabl,easy

%O 0,2

%A _N. J. A. Sloane_.