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).

1, -2, -2, -1, 4, 11, 16, 11, 3, -10, -55, -147, -215, -179, -80, -15, 34, 305, 1247, 2910, 4224, 3904, 2245, 735, 105, -154, -1949, -10971, -35970, -76269, -109554, -108184, -72639, -31780, -8190, -945, 874, 14297, 103679, 443762, 1255671, 2484619, 3535727, 3654132, 2726787, 1434797

Offset: 1

Author

André F. Labossière, Dec 06 2004

Keywords

• easy
• sign
• tabl

Examples

			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) + ...
= 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}
= 7^6 - 22*7^5 + 191*7^4 - 831*7^3 + 1891*7^2 - 2103*7 + 874
= 117649 - 369754 + 458591 - 285033 + 92659 - 14721 + 874 = 265.
		

Crossrefs

Cf. A101559, A000166, A000110, A101033, A101032, A000204, A100492, A099731, A000045, A094216, A094638, A000108.