A297195 - OEIS

A297195

Number of bitriangular permutations (row sums of A272644 if that triangle is prefixed with a row for n=1).

1, 1, 2, 7, 28, 133, 726, 4483, 30896, 235105, 1957930, 17712799, 172980804, 1813760317, 20323234814, 242353047355, 3064550705752, 40958281206169, 576917769130578, 8541793624670551, 132623408805525740, 2154730841214003061, 36560670776303600422, 646697046042017004787

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..24.

Irving Kaplansky and John Riordan, The problem of the rooks and its applications, Duke Mathematical Journal 13.2 (1946): 259-268. The array is on page 267.

Irving Kaplansky and John Riordan, The problem of the rooks and its applications, in Combinatorics, Duke Mathematical Journal, 13.2 (1946): 259-268. [Annotated scanned copy]

MAPLE

A297195 := proc(n)

if n = 1 then

else

add(A272644(n, m), m=1..n-1) ;

end if;

end proc:

seq(A297195(n), n=1..30) ; # R. J. Mathar, Mar 04 2018

MATHEMATICA

A272644[n_, m_] := Sum[StirlingS2[m+1, i+1] (-1)^(m-i) i^(n-m) i!, {i, 0, m}];

a[n_] := If[n == 1, 1, Sum[A272644[n, m], {m, 1, n-1}]];

Array[a, 24] (* Jean-François Alcover, Apr 03 2020 *)