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A098537
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Expansion of (1+x)^(1/3)/(1+x-18x^4)^(1/3).
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1
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1, 0, 0, 0, 6, -6, 6, -6, 78, -150, 222, -294, 1374, -3462, 6558, -10662, 30894, -82374, 180222, -339558, 811374, -2082534, 4875774, -10149702, 22872750, -55797126, 133232766, -294821286, 660771438, -1558556070, 3711070590
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Binomial transform is A098538.
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FORMULA
| a(n)=sum(b(j)*c(n-j,j,0,n), b(n)=if n=0 then 1 else sum(sum((if mod(n-4*k,3)=0 then binomial(k,(4*k-n)/3)*(-1)^((4*k-n)/3)*(18)^((n-k)/3) else 0)*(if k=m then (1/3)^k else m/k*(1/3)^k*sum(binomial(i,k-m-i)*(-1/3)^(k-m-i)*binomial(i+k-1,k-1),i,1,k-m)),k,m,n),m,1,n), c(n)=if n=0 then 1 else (-1)^(n+1)*if n=1 then (1/3)^n else 1/n*(1/3)^n*sum(binomial(k,n-1-k)*(-1/3)^(n-1-k)*binomial(k+n-1,n-1),k,1,n-1); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 06 2010]
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PROG
| (Other) a(n):=sum(b(j)*c(n-j, j, 0, n); b(n):=if n=0 then 1 else sum(sum((if mod(n-4*k, 3)=0 then binomial(k, (4*k-n)/3)*(-1)^((4*k-n)/3)*(18)^((n-k)/3) else 0)*(if k=m then (1/3)^k else m/k*(1/3)^k*sum(binomial(i, k-m-i)*(-1/3)^(k-m-i)*binomial(i+k-1, k-1), i, 1, k-m)), k, m, n), m, 1, n); c(n):=if n=0 then 1 else (-1)^(n+1)*if n=1 then (1/3)^n else 1/n*(1/3)^n*sum(binomial(k, n-1-k)*(-1/3)^(n-1-k)*binomial(k+n-1, n-1), k, 1, n-1); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 06 2010]
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CROSSREFS
| Cf. A098535.
Sequence in context: A054641 A024731 A195504 * A131703 A135357 A179415
Adjacent sequences: A098534 A098535 A098536 * A098538 A098539 A098540
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 13 2004
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