Search: id:A010843
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%I A010843
%S A010843 1,2,5,12,33,78,261,360,3681,13446,193509,1951452,23948865,
%T A010843 309740922,4341155877,65102989248,1041690874689,17708615729550,
%U A010843 318755470552389,6056352778233924,121127059051462881,2543668229620367298
%V A010843 1,-2,5,-12,33,-78,261,-360,3681,13446,193509,1951452,23948865,
%W A010843 309740922,4341155877,65102989248,1041690874689,17708615729550,
%X A010843 318755470552389,6056352778233924,121127059051462881,2543668229620367298
%N A010843 Incomplete Gamma Function at -3.
%D A010843 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 262.
%H A010843 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A010843 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 262.
%F A010843 E.g.f.: exp(-3x)/(1-x). - Michael Somos Mar 06 2004
%F A010843 a(0) = 1 and for n>0, a(n) is the permanent of the n X n matrix with 
               -2's on the diagonal and 1's elsewhere. a(n) = Sum(k=0..n, A008290(n, 
               k)*(-2)^k ). a(n) = Sum(k=0..n, A008279(n, k)*(-3)^(n-k) ). - DELEHAM 
               Philippe (kolotoko(AT)wanadoo.fr), Dec 15 2003
%p A010843 a:=n->n!*sum(((-3)^(k)/k!), k=0..n): seq(a(n), n=0..21); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2007
%t A010843 Table[ Gamma[ n, -3 ]*E^3, {n, 1, 24} ]
%o A010843 (PARI) a(n)=if(n<0,0,n!*polcoeff(exp(-3*x+x*O(x^n))/(1-x),n)) - Michael 
               Somos Mar 06 2004
%o A010843 (PARI) a(n)=local(A,p);if(n<1,n==0,A=matrix(n,n,i,j,1-3*(i==j));sum(i=1,
               n!,if(p=numtoperm(n,i),prod(j=1,n,A[j,p[j]])))) - Michael Somos Mar 
               06 2004
%Y A010843 See also A000023 A000166 A000142 A000522 A010842 A053486 A053487 A080954 
               A080955
%Y A010843 Cf. A008279 A008279 A089258.
%Y A010843 Sequence in context: A148284 A148285 A115523 this_sequence A084075 A000560 
               A032124
%Y A010843 Adjacent sequences: A010840 A010841 A010842 this_sequence A010844 A010845 
               A010846
%K A010843 sign
%O A010843 1,2
%A A010843 Simon Plouffe (simon.plouffe(AT)gmail.com)

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