A038166 G.f.: 1/((1-x)*(1-x^2))^6.
1, 6, 27, 92, 273, 714, 1715, 3816, 8007, 15938, 30381, 55692, 98735, 169806, 284349, 464672, 742950, 1164228, 1791426, 2710344, 4037670, 5928988, 8591154, 12294672, 17392258, 24337404, 33711510, 46251016, 62886162, 84779748
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (6, -9, -16, 60, -24, -116, 144, 66, -220, 66, 144, -116, -24, 60, -16, -9, 6, -1).
Programs
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Maple
A038166 := proc(n) add( A038163(n-i)*A038163(i),i=0..n) ; end proc: seq(A038166(n),n=0..30) ;# R. J. Mathar, Feb 22 2021
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Mathematica
CoefficientList[Series[1/((1-x)(1-x^2))^6,{x,0,40}],x] (* or *) LinearRecurrence[ {6,-9,-16,60,-24,-116,144,66,-220,66,144,-116,-24,60,-16,-9,6,-1},{1,6,27,92,273,714,1715,3816,8007,15938,30381,55692,98735,169806,284349,464672,742950,1164228},40] (* Harvey P. Dale, Jun 10 2013 *)
Formula
a(2*k) = binomial(k + 8, 8)*(2*k + 9)*(8*k^2 + 72*k + 55)/(11*5*9) = A059603(k); a(2*k + 1) = 2*binomial(k + 9, 9)*(8*k^2 + 80*k + 165)/(11*5) = 2*A059624(k), k >= 0; Wolfdieter Lang, Feb 02 2000
a(0)=1, a(1)=6, a(2)=27, a(3)=92, a(4)=273, a(5)=714, a(6)=1715, a(7)=3816, a(8)=8007, a(9)=15938, a(10)=30381, a(11)=55692, a(12)=98735, a(13)=169806, a(14)=284349, a(15)=464672, a(16)=742950, a(17)=1164228, a(n)=6*a(n-1)-9*a(n-2)-16*a(n-3)+60*a(n-4)-24*a(n-5)-116*a(n-6)+144*a(n-7)+ 66*a(n-8)- 220*a(n-9)+66*a(n-10)+144*a(n-11)-116*a(n-12)-24*a(n-13)+60*a(n-14)-16*a(n-15)- 9*a(n-16)+ 6*a(n-17)-a(n-18). - Harvey P. Dale, Jun 10 2013