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A172047
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n*(n+1)*(15*n^2-n-8)/12.
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1
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0, 1, 25, 124, 380, 905, 1841, 3360, 5664, 8985, 13585, 19756, 27820, 38129, 51065, 67040, 86496, 109905, 137769, 170620, 209020, 253561, 304865, 363584, 430400, 506025, 591201, 686700, 793324, 911905, 1043305, 1188416, 1348160, 1523489
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OFFSET
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0,3
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COMMENTS
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This is the case d=5 in the general formula n*(n*(n+1)*(2*d*n-2*d+3)/6)-sum(i=0..n-1, i*(i+1)*(2*d*i-2*d+3)/6) = n*(n+1)*(3*d*n^2-d*n+4*n-2*d+2)/12. - Bruno Berselli, Dec 07 2010
The inverse binomial transform yields 0, 1, 23, 52, 30, 0, 0 (0 continued). - R. J. Mathar, Dec 09 2010
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LINKS
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B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
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FORMULA
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G.f.: -x*(1+20*x+9*x^2)/(x-1)^5. - R. J. Mathar, Dec 09 2010
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MATHEMATICA
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CoefficientList[Series[x (1 + 20 x + 9 x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 01 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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