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A122898
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Expansion of (sqrt(21x^2-10x+1)+7x-1)/(2x(1-7x)).
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4
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1, 6, 37, 233, 1491, 9660, 63195, 416610, 2763595, 18426026, 123375927, 829053197, 5588050069, 37764371676, 255800207277, 1736181639585, 11804962371795, 80394249836010, 548283258074895, 3744067955618403, 25596986050620681
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 3rd binomial transform of C(2n+1,n+1) (A001700); 5th binomial transform of C(n,floor(n/2)) (A001405); 7th binomial transform of (-1)^n*A000108(n)=A168491(n). Hankel transform is (1,1,1,.....). Row sums of Riordan array (1/(1+5x+x^2),x/(1+5x+x^2))^(-1). Counts Motzkin paths with 5 colors for horizontal steps. [Corrected by Philippe DELEHAM, Nov 29 2009]
Binomial transform of A005573. 7th binomial transform of A168491. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2009]
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FORMULA
| a(n)=sum{k=0..n, 3^(n-k)C(n,k)C(2k+1,k+1)}; a(n)=sum{k=0..n, 5^(n-k)C(n,k)C(k,floor(k/2))}; a(n)=sum{k=0..n, 7^(n-k)C(n,k)*(-1)^k*C(k)} where C(n)=A000108(n); a(n)=sum{k=0..n, sum{j=0..n, 3^(n-j)*C(n,k)*C(n-k,j-k)*C(j+1,k+1)}}.
G.f.: 1/(1-6x-x^2/(1-5x-x^2/(1-5x-x^2/(1-5x-x^2/(1-...(continued fraction). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2009]
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CROSSREFS
| Sequence in context: A076026 A161734 A081570 * A081912 A081188 A154623
Adjacent sequences: A122895 A122896 A122897 * A122899 A122900 A122901
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 18 2006
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