Search: id:A129779
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%I A129779
%S A129779 1,1,2,6,30,210,1890,20790,270270,4054050,68918850,1309458150,
%T A129779 27498621150,632468286450,15811707161250,426916093353750,
%U A129779 12380566707258750,383797567925021250,12665319741525701250
%V A129779 1,-1,2,-6,30,-210,1890,-20790,270270,-4054050,68918850,-1309458150,27498621150,
%W A129779 -632468286450,15811707161250,-426916093353750,12380566707258750,-383797567925021250,
%X A129779 12665319741525701250
%N A129779 a(1) = 1, a(2) = -1, a(3) = 2; for n > 3, a(n) = -(2*n-5)*a(n-1).
%C A129779 a(n) = (-1)^(n-1)*A097801(n-2) = (-1)^(n-1)*(2*(n-2))!/((n-2)!*2^(n-3)) 
               for n > 2.
%C A129779 Sequence is also the first column of the inverse of the infinite lower 
               triangular matrix M, where M(j,k) = 1+2*(k-1)*(j-k) for k < j, M(j,
               k) = 1 for k = j, M(j,k) = 0 for k > j.
%C A129779 Upper left 6x6 submatrix of M is
%C A129779 [1 0 0 0 0 0]
%C A129779 [1 1 0 0 0 0]
%C A129779 [1 3 1 0 0 0]
%C A129779 [1 5 5 1 0 0]
%C A129779 [1 7 9 7 1 0]
%C A129779 [1 9 13 13 9 1],
%C A129779 and upper left 6x6 submatrix of M^-1 is
%C A129779 [ 1 0 0 0 0 0]
%C A129779 [ -1 1 0 0 0 0]
%C A129779 [ 2 -3 1 0 0 0]
%C A129779 [ -6 10 -5 1 0 0]
%C A129779 [ 30 -50 26 -7 1 0]
%C A129779 [ -210 350 -182 50 -9 1].
%C A129779 Row sums of M are 1, 2, 5, 12, 25, 46, ... (see A116731); diagonal sums 
               of M are 1, 1, 2, 4, 7, 13, 20, 32, 45, 65, 86, 116, 147, 189, ... 
               with first differences 0, 1, 2, 3, 6, 7, 12, 13, 20, 21, 30, 31, 
               42, ... and second differences 1, 1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 
               ... (see A093178).
%t A129779 a[n_] := -(2 n - 5) a[n - 1]; a[1] = 1; a[2] = -1; a[3] = 2; Array[a, 
               20] (* Robert G. Wilson v *)
%o A129779 (PARI) {m=19; print1(1, ",", -1, ","); print1(a=2, ","); for(n=4, m, 
               k=-(2*n-5)*a; print1(k, ","); a=k)} /* Klaus Brockhaus, May 21 2007 
               */
%o A129779 (PARI) {print1(1, ",", -1, ","); for(n=3, 19, print1((-1)^(n-1)*(2*(n-2))!/
               ((n-2)!*2^(n-3)), ","))} /* Klaus Brockhaus, May 21 2007 */
%o A129779 (PARI) {m=19; M=matrix(m, m, j, k, if(k>j, 0, if(k==j, 1, 1+2*(k-1)*(j-k)))); 
               print((M^-1)[, 1]~)} /* Klaus Brockhaus, May 21 2007 */
%o A129779 (MAGMA) m:=19; M:=Matrix(IntegerRing(), m, m, [< j, k, Maximum(0, 1+2*(k-1)*(j-k)) 
               > : j, k in [1..m] ] ); Transpose(ColumnSubmatrix(M^-1, 1, 1)); /
               * Klaus Brockhaus, May 21 2007 */
%Y A129779 Cf. A097801, A116731, A093178.
%Y A129779 Sequence in context: A104561 A127482 A118747 this_sequence A068215 A096775 
               A002110
%Y A129779 Adjacent sequences: A129776 A129777 A129778 this_sequence A129780 A129781 
               A129782
%K A129779 sign
%O A129779 1,3
%A A129779 Paul Curtz (bpcrtz(AT)free.fr), May 17 2007
%E A129779 Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) 
               and Robert G. Wilson v (rgwv(AT)rgwv.com), May 21 2007

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