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

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

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;

Mathematica

nn = 10; Map[Select[#, # > 0 &] &, Range[0, nn]! CoefficientList[
Series[Exp[7 x + 7 y x] Exp[ x], {x, 0, nn}], {x, y}]] // Grid (* Geoffrey Critzer, Jan 11 2016 *)

Crossrefs

Cf. A038207, A038233

Sequence in context: A317231 A237646 A288188 * A354546 A261117 A098432

Adjacent sequences: A038282 A038283 A038284 * A038286 A038287 A038288

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane.

Status

approved