A038285 - OEIS

A038285

Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*7^j.

1, 8, 7, 64, 112, 49, 512, 1344, 1176, 343, 4096, 14336, 18816, 10976, 2401, 32768, 143360, 250880, 219520, 96040, 16807, 262144, 1376256, 3010560, 3512320, 2304960, 806736, 117649, 2097152, 12845056, 33718272, 49172480

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OFFSET

0,2

COMMENTS

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

REFERENCES

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

R.P. Stanley, Enumerative Combinatorics Vol I, Cambridge Univ. Press,1997, page 11.

LINKS

Table of n, a(n) for n=0..31.

FORMULA

E.g.f.: exp(8*x + 7*y*x) - Geoffrey Critzer, Jan 11 2016

EXAMPLE

8, 7;

64, 112, 49;

512, 1344, 1176, 343;

4096, 14336, 18816, 10976, 2401;

32768, 143360, 250880, 219520, 96040, 16807;

262144, 1376256, 3010560, 3512320, 2304960, 806736, 117649;