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A279127
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a(n) = Sum_{0<=m<n} Product_{-m<=j<=m} (n-j).
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1
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0, 1, 8, 147, 5824, 405845, 43733976, 6726601063, 1398047697152, 377278848390249, 128228860181918440, 53585748788874537851, 27001973543813627400768, 16144773936121968789213757, 11300021011239061076228900024, 9152162639827097780662174019535
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OFFSET
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0,3
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COMMENTS
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n-m | a(n)-a(m) for all n,m.
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LINKS
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FORMULA
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a(n) = n*hypergeom([1,n+1,1-n],[],-1).
a(n+3) = -a(n)+(4*n^2+6*n-1)*a(n+1)+(4*n^2+18*n+17)*a(n+2)+8*n+12.
D-finite with recurrence +(-2*n+5)*a(n) +(2*n-5)*(4*n^2-6*n+1)*a(n-1) -(2*n-1)*(4*n^2-18*n+19)*a(n-2) +(2*n-1)*a(n-3)=0. - R. J. Mathar, Jul 27 2022
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MAPLE
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f:= n -> add(mul(n-m, m=-k..k), k=0..n):
map(f, [$0..40]);
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MATHEMATICA
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Table[Sum[Product[n - j, {j, -m, m}], {m, 0, n}], {n, 0, 25}] (* G. C. Greubel, Dec 07 2016 *)
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PROG
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(PARI) a(n) = sum(m=0, n-1, prod(j=-m, m, n-j)); \\ Michel Marcus, Dec 07 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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