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A102411
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Even triangle !n. This table read by rows gives the coefficients of sum formulae of n-th Left factorials (A003422). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies !n = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!.
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0, 1, 0, -16, 5, 1, 0, 5256, -3068, 276, 32, 0, 2070720, 2367420, -912150, 53220, 3510, 0, -36031524480, 15327895296, -40587120, -387492840, 21414120, 758184, 840, -212459319878400, -75473246681280, 38182549456800, -2562251680800, -195611371200, 13639812480, 285616800, 453600
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Incidently, the sum of signed coefficients for each k-th row is divisible by (2*k-2)!. Moreover, another variant but an incomplete one and sorted differently of the above sequence is presented in A101752.
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EXAMPLE
| !11=4037914; 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 = [ -212459319878400 -75473246681280*11 +38182549456800*11^2 -2562251680800*11^3
-195611371200*11^4 +13639812480*11^5 +285616800*11^6 +453600*11^7 ]/10! = 4037914.
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CROSSREFS
| Cf. A102412, A094638, A094216, A003422, A008276, A101752, A102409, A102410, A101751, A000142, A101559, A101032, A099731.
Sequence in context: A177499 A040247 A089083 * A040245 A070538 A198064
Adjacent sequences: A102408 A102409 A102410 * A102412 A102413 A102414
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Andre F. Labossiere (boronali(AT)laposte.net), Jan 07 2005
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