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A101560 Triangle read by rows giving the coefficients of general sum formulas 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).

%I A101560 #9 Jun 16 2016 23:27:26
%S A101560 1,-2,-2,-1,4,11,16,11,3,-10,-55,-147,-215,-179,-80,-15,34,305,1247,
%T A101560 2910,4224,3904,2245,735,105,-154,-1949,-10971,-35970,-76269,-109554,
%U A101560 -108184,-72639,-31780,-8190,-945,874,14297,103679,443762,1255671,2484619,3535727,3654132,2726787,1434797
%N A101560 Triangle read by rows giving the coefficients of general sum formulas 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).
%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) + 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.
%K A101560 easy,sign,tabl
%O A101560 1,2
%A A101560 _André F. Labossière_, Dec 06 2004