The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A038285 Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*7^j. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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 * A261117 A098432 A197623 Adjacent sequences:  A038282 A038283 A038284 * A038286 A038287 A038288 KEYWORD nonn,tabl,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)