A025999 Expansion of g.f. 1/((1-2*x) * (1-5*x) * (1-8*x) * (1-11*x)).
1, 26, 445, 6370, 82901, 1019746, 12105885, 140404290, 1603014501, 18104952866, 202945103725, 2262802497410, 25134485221301, 278430633932386, 3078357517755965, 33986947913921730, 374856803115095301, 4131429114327366306, 45509760855920174605, 501119725990818613250
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (26,-231,806,-880).
Programs
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Mathematica
CoefficientList[Series[1/((1-2x)(1-5x)(1-8x)(1-11x)),{x,0,20}],x] (* or *) LinearRecurrence[{26,-231,806,-880},{1,26,445,6370},20] (* Harvey P. Dale, May 24 2014 *)
Formula
a(n) = -4*2^n/81 +125*5^n/54 -256*8^n/27 +1331*11^n/162. - R. J. Mathar, Jun 20 2013
a(0)=1, a(1)=26, a(2)=445, a(3)=6370, a(n)=26*a(n-1)-231*a(n-2)+ 806*a(n-3)- 880*a(n-4). - Harvey P. Dale, May 24 2014
From Seiichi Manyama, May 04 2025: (Start)
a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(n+3,k+3) * Stirling2(k+3,3).
a(n) = Sum_{k=0..n} (-3)^k * 11^(n-k) * binomial(n+3,k+3) * Stirling2(k+3,3). (End)
E.g.f.: exp(2*x)*(1331*exp(9*x) - 1536*exp(6*x) + 375*exp(3*x) - 8)/162. - Stefano Spezia, May 04 2025