cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A079510 Triangle T(n,k) read by rows; related to number of preorders.

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%I A079510 #27 Jan 18 2019 04:40:52
%S A079510 1,0,2,0,3,6,0,0,20,24,0,0,15,130,120,0,0,0,210,924,720,0,0,0,105,
%T A079510 2380,7308,5040,0,0,0,0,2520,26432,64224,40320,0,0,0,0,945,44100,
%U A079510 303660,623376,362880,0,0,0,0,0,34650,705320,3678840,6636960,3628800
%N A079510 Triangle T(n,k) read by rows; related to number of preorders.
%C A079510 There are only m nonzero entries in the m-th column.
%H A079510 G. C. Greubel, <a href="/A079510/b079510.txt">Rows n=1..30 of triangle, flattened</a>
%H A079510 G. Kreweras, <a href="http://www.numdam.org/item?id=MSH_1976__53__5_0">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30. (See the array on page 29.)
%H A079510 G. Kreweras, <a href="/A019538/a019538.pdf">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)
%e A079510 Triangle begins:
%e A079510   1;
%e A079510   0,   2;
%e A079510   0,   3,   6;
%e A079510   0,   0,  20,  24;
%e A079510   0,   0,  15, 130, 120;
%e A079510   ...
%t A079510 T[n_, k_]:= If[k < 1 || k > n, 0, If[n==1 && k==1, 1, n*(T[n-1, k-1] + T[n-2, k-1])]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* _G. C. Greubel_, Jan 17 2019 *)
%o A079510 (PARI) T(n,k)=if(k<=0 || k>n, 0, if(n==1 && k==1, 1, n*(T(n-1,k-1)+T(n-2,k-1))));
%Y A079510 A rearrangement of the triangle in A008306. - _Benoit Cloitre_, Jan 27 2003
%K A079510 nonn,tabl
%O A079510 1,3
%A A079510 _N. J. A. Sloane_, Jan 21 2003
%E A079510 Recurrence and more terms from _Michael Somos_, Jan 23 2003
%E A079510 Offset changed to 1 by _G. C. Greubel_, Jan 17 2019