A059598 Tenth column (m=9) of convolution triangle A059594(n,m).
1, 10, 65, 320, 1320, 4752, 15400, 45760, 126500, 328680, 809380, 1901120, 4282200, 9289840, 19482200, 39619008, 78337930, 150954980, 284060810, 522920640, 943206264, 1669294000, 2902420600, 4963400000
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (10, -35, 20, 195, -498, -15, 1800, -2205, -2150, 7001, -2260, -9785, 10830, 4845, -15504, 4845, 10830, -9785, -2260, 7001, -2150, -2205,1800, -15, -498, 195, 20, -35, 10, -1).
Programs
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Mathematica
CoefficientList[Series[1/((1-x^2)(1-x))^10,{x,0,30}],x] (* or *) LinearRecurrence[{10,-35,20,195,-498,-15,1800,-2205,-2150,7001,-2260,-9785,10830,4845,-15504,4845,10830,-9785,-2260,7001,-2150,-2205,1800,-15,-498,195,20,-35,10,-1},{1,10,65,320,1320,4752,15400,45760,126500,328680,809380,1901120,4282200,9289840,19482200,39619008,78337930,150954980,284060810,522920640,943206264,1669294000,2902420600,4963400000,8356661300,13865072520,22688862900,36646948800,58465921800,92190872400},30] (* Harvey P. Dale, Oct 20 2021 *)
Formula
G.f.: 1/((1-x^2)*(1-x))^10.
a(2*k)= binomial(n+14, 14)*(2*n+15)*(8*n^4+240*n^3+2185*n^2+5775*n+2907)/(19*9*17*15);
a(2*k+1)= binomial(k+15, 15)*2*(8*k^4+256*k^3+2767*k^2+11504*k+14535)/(17*9*19), k >= 0