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A193668
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a(n) = Sum_{i=0..n-1} (n+i)*a(n-1-i) for n>1, a(0)=1, a(1)=1.
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3
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1, 1, 5, 24, 134, 866, 6392, 53198, 493628, 5057522, 56741240, 692118422, 9122245508, 129220379978, 1958059133552, 31607140330670, 541515698082332, 9814691158604258, 187629572002767848, 3773371262361852422, 79636835475910932020
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OFFSET
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0,3
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COMMENTS
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Occurs in making the Q-residue A193657.
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LINKS
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FORMULA
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a(n) = (n-n^2-1)*Gamma(n) + e*(n*Gamma(n+1,1)-(n-1)*Gamma(n,1)) for n>0. - Peter Luschny, May 30 2014.
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MAPLE
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a := n -> `if`(n=0, 1, (n-n^2-1)*GAMMA(n)+exp(1)*((1-n)*GAMMA(n, 1) + n*GAMMA(n+1, 1))): seq(simplify(a(n)), n=0..20); # Peter Luschny, May 30 2014
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MATHEMATICA
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Flatten[{1, RecurrenceTable[{(n-2)*a[n-2] - (n+2)*a[n-1] + a[n] == 0, a[1]==1, a[2]==5}, a, {n, 20}]}] (* Vaclav Kotesovec, Nov 20 2012 *)
CoefficientList[Series[Log[x-1]+E*Gamma[0, 1-x]-E*Gamma[0, 1]+1-I*Pi+(E^x*x-x^2)/(x-1)^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 20 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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