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 A102410 Odd triangle n!. This table read by rows gives the coefficients of sum formulas of n-th Factorials (A000142). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+3+(-1)^n]/4 and T(i,k) satisfies n! = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!. 3
 1, 0, 0, -6, 3, 1, 0, 2400, -2024, 264, 32, 0, 2570400, 909720, -666540, 55800, 3420, 0, -19071521280, 12195884736, -762499920, -282106440, 22425480, 741384, 840, -219303218534400, -11953192930560, 27128332828800, -2808016545600, -125442525600, 14164990560, 280576800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Incidentally, the sum of signed coefficients for each k-th row is divisible by (2*k-2)!. LINKS EXAMPLE Triangle starts: 1, 0, 0; -6, 3, 1, 0; 2400, -2024, 264, 32, 0; 2570400, 909720, -666540, 55800, 3420, 0; -19071521280, 12195884736, -762499920, -282106440, 22425480, 741384, 840; ... 11!=39916800; substituting n=11 in the formula of the k-th row we obtain k=6 and the coefficients T(i,6) are those needed for computing 11!. => 11! = [ -219303218534400 -11953192930560*11 +27128332828800*11^2 -2808016545600*11^3 -125442525600*11^4 +14164990560*11^5 +280576800*11^6 +453600*11^7 ]/10! = 39916800. CROSSREFS Cf. A102409, A008276, A094216, A000142, A094638, A101751, A102411, A102412, A101752, A003422, A101559, A101032, A099731. Sequence in context: A119923 A204420 A331570 * A105123 A058291 A132615 Adjacent sequences:  A102407 A102408 A102409 * A102411 A102412 A102413 KEYWORD sign,tabf,uned AUTHOR André F. Labossière, Jan 07 2005 STATUS approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)