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.

A049055 Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (1 <= k <= n).

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%I A049055 #25 Feb 18 2021 09:22:52
%S A049055 1,1,2,1,12,6,1,50,132,24,1,180,1830,1560,120,1,602,20460,60960,20520,
%T A049055 720,1,1932,201726,1856400,2047920,302400,5040,1,6050,1832292,
%U A049055 48550824,155801520,72586080,4979520,40320,1,18660,15717750,1144994760,10006131240,13069123200,2767474080,91082880,362880
%N A049055 Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (1 <= k <= n).
%H A049055 R. J. Clarke, <a href="http://dx.doi.org/10.1016/0012-365X(90)90146-9">Covering a set by subsets</a>, Discrete Math., 81 (1990), 147-152.
%F A049055 T(n,k) = A035348(n,k)*k!, the order in which we cover the n-set is considered. - _Geoffrey Critzer_, Jun 28 2013
%e A049055 Triangle starts
%e A049055   1;
%e A049055   1,   2;
%e A049055   1,  12,   6;
%e A049055   1,  50, 132,  24;
%e A049055   ...
%t A049055 t[n_, k_] := Sum[ (-1)^i*Binomial[k, i]*(2^k - 1 - i)^n, {i, 0, k}]; Flatten[ Join[{1}, Table[t[n, k], {n, 1, 9}, {k, 1, n}]]] (* _Jean-François Alcover_, Dec 12 2011, after _Michael Somos_ *)
%o A049055 (PARI) {T(n, k)=sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n)} /* _Michael Somos_, Oct 16 2006 */
%Y A049055 Row sums are A049056.
%Y A049055 Cf. A035348.
%K A049055 nonn,tabl,easy,nice
%O A049055 1,3
%A A049055 _N. J. A. Sloane_, _Michael Somos_