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A107600 Column 5 of array illustrated in A089574 and related to A034261.

%I A107600 #12 Jul 31 2015 17:52:34
%S A107600 1,18,101,357,978,2274,4711,8954,15915,26806,43197,67079,100932,
%T A107600 147798,211359,296020,406997,550410,733381,964137,1252118,1608090,
%U A107600 2044263,2574414,3214015,3980366,4892733,5972491,7243272,8731118,10464639
%N A107600 Column 5 of array illustrated in A089574 and related to A034261.
%C A107600 The sequences in A089574 count ordered partitions. Sequence A001296 can be associated with 9 = 3+3+3. Six times sequence A005585, associated with 10 = 3+3+2+2. The other three sequences comprising A107600 are generated in A034261 and can be associated with 10 = 5 + 5 = 4 + 4 + 2 = 2 + 2 + 2 + 2 + 2.
%H A107600 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A107600 G.f.: (x^5 -5*x^4 +7*x^3 +4*x^2 -11*x -1) *x^9 /(x-1)^7. - _Alois P. Heinz_, Nov 06 2009
%e A107600 A107600(n) can be constructed from five other sequences as follows:
%e A107600 1...7...25...65...140.......A001296
%e A107600 ....1...11...56...196.......A034264
%e A107600 ....6...42..162...462.......6.*.A005585.
%e A107600 ....3...18...60...150.......A006011
%e A107600 ....1....5...14....30.......A000330
%e A107600 therefore
%e A107600 1..18..101..357...978.......A107600
%p A107600 a:= n-> `if` (n<9, 0, (92292 +(-6580 +(-5745 +(1535 +(-147+5*n) *n) *n) *n) *n) *n /720 -218): seq(a(n), n=9..45); # _Alois P. Heinz_, Nov 06 2009
%t A107600 Select[CoefficientList[Series[(x^5-5x^4+7x^3+4x^2-11x-1)x^9/(x-1)^7, {x,0,50}],x],#>0&] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1,18,101,357,978,2274,4711},42] (* _Harvey P. Dale_, May 01 2011 *)
%Y A107600 Cf. A034261, A089574, A000330, A001296, A005585, A006011, A034264.
%K A107600 easy,nonn
%O A107600 9,2
%A A107600 _Alford Arnold_, May 17 2005
%E A107600 More terms from _Alois P. Heinz_, Nov 06 2009