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 A179457 Triangle read by rows: number of permutation trees of power n and width <= k. 2
 1, 1, 2, 1, 5, 6, 1, 12, 23, 24, 1, 27, 93, 119, 120, 1, 58, 360, 662, 719, 720, 1, 121, 1312, 3728, 4919, 5039, 5040, 1, 248, 4541, 20160, 35779, 40072, 40319, 40320, 1, 503, 15111, 103345, 259535, 347769, 362377, 362879, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Partial row sums of A008292 (triangle of Eulerian numbers). Given by a very similar formula. Special case: A179457(n,2) = A000325(n) for n > 1 (Grassmannian permutations). REFERENCES Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 533. LINKS Peter Luschny, Permutation Trees. FORMULA T(n,k) = sum( ((-1)^j*(k-j)^(n+1))*binomial(n+1,j),j=0..k) - Olivier Gérard, Aug 04 2012 EXAMPLE 1; 1, 2; 1, 5, 6; 1, 12, 23, 24; 1, 27, 93, 119, 120; 1, 58, 360, 662, 719, 720; 1, 121, 1312, 3728, 4919, 5039, 5040; 1, 248, 4541, 20160, 35779, 40072, 40319, 40320; 1, 503, 15111, 103345, 259535, 347769, 362377, 362879, 362880; MAPLE Eulerian:= (n, k)-> sum((-1)^j*(k-j+1)^n * binomial(n+1, j), j=0..k+1): s:=(j, n)-> sum(Eulerian(j, k-1), k=1..n): for i from 1 to 15 do print(seq(s(i, n), n=1..i)) od; # Gary Detlefs, Nov 18 2011 MATHEMATICA Flatten[Table[Table[Sum[(-1)^j (k-j)^(n+1) Binomial[n+1, j], {j, 0, k}], {k, 1, n + 1}], {n, 0, 10}], 1] (* Olivier Gérard, Aug 04 2012 *) CROSSREFS Cf. A008292. Row sums sequence is 1,3,12,... A001710(n+1) = (n+1)!/2. - Olivier Gérard, Aug 04 2012 Sequence in context: A241168 A145324 A260613 * A107783 A047887 A120986 Adjacent sequences:  A179454 A179455 A179456 * A179458 A179459 A179460 KEYWORD nonn,tabl AUTHOR Peter Luschny, Aug 11 2010 STATUS approved

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Last modified October 14 07:06 EDT 2019. Contains 327995 sequences. (Running on oeis4.)