%I A101560
%S A101560 1,2,2,1,4,11,16,11,3,10,55,147,215,179,80,15,34,305,1247,2910,4224,3904,
%T A101560 2245,735,105,154,1949,10971,35970,76269,109554,108184,72639,31780,8190,
               945,
%U A101560 874,14297,103679,443762,1255671,2484619,3535727,3654132,2726787,1434797
%V A101560 1,-2,-2,-1,4,11,16,11,3,-10,-55,-147,-215,-179,-80,-15,34,305,1247,2910,
               4224,3904,
%W A101560 2245,735,105,-154,-1949,-10971,-35970,-76269,-109554,-108184,-72639,-31780,
               -8190,-945,
%X A101560 874,14297,103679,443762,1255671,2484619,3535727,3654132,2726787,1434797
%N A101560 Triangle read by rows giving the coefficients of general sum formulae 
               of n-th Subfactorial numbers (A000166). The k-th row (k>=1) contains 
               T(i,k) for i=1 to 2*k-1, where T(i,k) satisfies Subf(n) = Sum_{k=1..n} 
               Sum_{i=1..2*k-1} T(i,k) * C(n-k,i-1) * n^(n-k).
%H A101560 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A101560 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%e A101560 Subf(7) = 7^(7 - 1) - {2 + 2*(7 - 2) + C(7 - 2,2)}*7^(7 - 2) + {4 + 11*(7 
               - 3) + 16*C(7 - 3,2) + 11*C(7 - 3,3)
%e A101560 + 3*C(7 - 3,4)}*7^(7 - 3) - {10 + 55*(7 - 4) + 147*C(7 - 4,2) + 215*C(7 
               - 4,3)}*7^(7 - 4) + ...
%e A101560 = 7^6 - {2 + 10 + 10}*7^5 + {4 + 44 + 96 + 44 + 3}*7^4 - {10 + 165 + 
               441 + 215}*7^3 + {34 + 610 + 1247}*7^2 - {154 + 1949}*7 + {874}
%e A101560 = 7^6 - 22*7^5 + 191*7^4 - 831*7^3 + 1891*7^2 - 2103*7 + 874
%e A101560 = 117649 - 369754 + 458591 - 285033 + 92659 - 14721 + 874 = 265.
%Y A101560 Cf. A101559, A000166, A000110, A101033, A101032, A000204, A100492, A099731, 
               A000045, A094216, A094638, A000108.
%Y A101560 Sequence in context: A158985 A087854 A086873 this_sequence A010243 A123398 
               A102849
%Y A101560 Adjacent sequences: A101557 A101558 A101559 this_sequence A101561 A101562 
               A101563
%K A101560 easy,sign,tabl
%O A101560 1,2
%A A101560 Andre F. Labossiere (boronali(AT)laposte.net), Dec 06 2004