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%I #12 Jan 11 2016 21:00:09
%S 1,8,7,64,112,49,512,1344,1176,343,4096,14336,18816,10976,2401,32768,
%T 143360,250880,219520,96040,16807,262144,1376256,3010560,3512320,
%U 2304960,806736,117649,2097152,12845056,33718272,49172480
%N Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*7^j.
%C T(i,j) is the number of sequences (X_1, X_2, X_3, X_4) of subsets of {1,2,...,i} such that X_1 intersect X_2 intersect X_3 intersect X_4 is empty and X_4 contains exactly j elements. Cf. Stanley reference. - Geoffrey Critzer, Jan 11 2016
%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.
%D R.P. Stanley, Enumerative Combinatorics Vol I, Cambridge Univ. Press,1997, page 11.
%F E.g.f.: exp(8*x + 7*y*x) - _Geoffrey Critzer_, Jan 11 2016
%e 1;
%e 8, 7;
%e 64, 112, 49;
%e 512, 1344, 1176, 343;
%e 4096, 14336, 18816, 10976, 2401;
%e 32768, 143360, 250880, 219520, 96040, 16807;
%e 262144, 1376256, 3010560, 3512320, 2304960, 806736, 117649;
%t nn = 10; Map[Select[#, # > 0 &] &,Range[0, nn]! CoefficientList[
%t Series[Exp[7 x + 7 y x] Exp[ x], {x, 0, nn}], {x, y}]] // Grid (* _Geoffrey Critzer_, Jan 11 2016 *)
%Y Cf. A038207, A038233
%K nonn,tabl,easy
%O 0,2
%A _N. J. A. Sloane_.
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