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 A232187 Number T(n,k) of parity alternating permutations of [n] with exactly k descents from odd to even numbers; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-1)/2)), read by rows. 2
 1, 1, 2, 1, 1, 5, 3, 2, 8, 2, 20, 44, 8, 6, 66, 66, 6, 114, 594, 414, 30, 24, 624, 1584, 624, 24, 864, 8784, 14544, 4464, 144, 120, 6840, 36240, 36240, 6840, 120, 8280, 147720, 471120, 353520, 55320, 840, 720, 86400, 857520, 1739520, 857520, 86400, 720, 96480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(2n+1,k) = T(2n+1,n-k). T(2n+2,n) = T(2n+1,n) + T(2n+3,n+1). LINKS Alois P. Heinz, Rows n = 0..29, flattened FORMULA T(2n+1,k) = n! * A173018(n+1,k) = A000142(n) * A173018(n+1,k). EXAMPLE T(5,0) = 2: 12345, 34125. T(5,1) = 8: 12543, 14325, 14523, 32145, 34521, 52143, 52341, 54123. T(5,2) = 2: 32541, 54321. T(6,2) = 8: 163254, 165432, 321654, 325416, 541632, 543216, 632541, 654321. T(7,0) = 6: 1234567, 1256347, 3412567, 3456127, 5612347, 5634127. T(7,1) = 66: 1234765, 1236547, 1236745, ..., 7456123, 7612345, 7634125. T(7,2) = 66: 1254763, 1276543, 1432765, ..., 7652143, 7652341, 7654123. T(7,3) = 6: 3254761, 3276541, 5432761, 5476321, 7632541, 7654321. Triangle T(n,k) begins: :  0 :   1; :  1 :   1; :  2 :   2; :  3 :   1,    1; :  4 :   5,    3; :  5 :   2,    8,     2; :  6 :  20,   44,     8; :  7 :   6,   66,    66,     6; :  8 : 114,  594,   414,    30; :  9 :  24,  624,  1584,   624,   24; : 10 : 864, 8784, 14544,  4464,  144; : 11 : 120, 6840, 36240, 36240, 6840, 120; CROSSREFS Column k=0 gives: A199660. Row sums give: A092186 (for n>0). T(2n+1,n) = A000142(n). T(2n+2,n) = A001048(n+1). Sequence in context: A263296 A259862 A182930 * A076241 A316399 A139347 Adjacent sequences:  A232184 A232185 A232186 * A232188 A232189 A232190 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Nov 20 2013 STATUS approved

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Last modified August 5 18:00 EDT 2021. Contains 346488 sequences. (Running on oeis4.)