%I A008291
%S A008291 1,2,3,9,8,6,44,45,20,10,265,264,135,40,15,1854,1855,924,315,70,21,
%T A008291 14833,14832,7420,2464,630,112,28,133496,133497,66744,22260,5544,1134,
%U A008291 168,36,1334961,1334960,667485,222480,55650,11088,1890,240,45,14684570
%N A008291 Triangle of rencontres numbers.
%C A008291 T(n,k) = number of permutations of n elements with k fixed points.
%D A008291 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990, p. 194.
%D A008291 I. Kaplansky, Symbolic solution of certain problems in permutations, 
               Bull. Amer. Math. Soc., 50 (1944), 906-914.
%D A008291 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               65.
%e A008291 Triangle begins:
%e A008291 1
%e A008291 2 3
%e A008291 9 8 6
%e A008291 44 45 20 10
%e A008291 265 264 135 40 15
%e A008291 1854 1855 924 315 70 21
%e A008291 14833 14832 7420 2464 630 112 28
%e A008291 133496 133497 66744 22260 5544 1134 168 36
%o A008291 (PARI) {T(n, k)= if(k<0|k>n, 0, n!/k!*sum(i=0, n-k, (-1)^i/i!))}
%Y A008291 T(n, k)=binomial(n, k)*A000166(n-k). Cf. A008290.
%Y A008291 Diagonals give A000217, A007290, A060008, A060836, A000166, A000240, 
               A000387, A000449, A000475.
%Y A008291 Sequence in context: A021421 A152812 A086565 this_sequence A122665 A133066 
               A131988
%Y A008291 Adjacent sequences: A008288 A008289 A008290 this_sequence A008292 A008293 
               A008294
%K A008291 nonn,tabl,nice,easy
%O A008291 2,2
%A A008291 N. J. A. Sloane (njas(AT)research.att.com).
%E A008291 Comments and more terms from Michael Somos, Apr 26 2000.