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A128387
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Expansion of c(5x^2)/(1-xc(5x^2)), where c(x) is the g.f. of A000108.
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5
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1, 1, 6, 11, 66, 146, 876, 2131, 12786, 32966, 197796, 530526, 3183156, 8786436, 52718616, 148733571, 892401426, 2561439806, 15368638836, 44731364266, 268388185596, 790211926076, 4741271556456, 14095578557486
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Hankel transform is 5^C(n+1,2). Reversion of x(1+x)/(1+2x+6x^2).
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FORMULA
| G.f.: (sqrt(1-20x^2)+2x-1)/(2x(1-6x)); a(n)=(1/(n+1))sum{k=0..n+1, sum{j=0..k, C(n,k)C(k,j)C(2n-2k+j,n-2k+j)(-1)^(n-2k+j)*2^j*6^(k-j)}}; a(n)=sum{k=0..floor(n/2), C(n,n-k)*(n-2k+1)*5^k/(n-k+1)}; a(n)=sum{k=0..floor(n/2), A009766(n-k,k)*5^k};
a(n)=Sum_{k, 0<=k<=n}5^k*A120730(n,n-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007
Conjecture: (n+1)*a(n) -6*(n+1)*a(n-1) +20*(2-n)*a(n-2) +120*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 14 2011
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CROSSREFS
| Sequence in context: A152448 A073219 A110445 * A061519 A193664 A080875
Adjacent sequences: A128384 A128385 A128386 * A128388 A128389 A128390
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 28 2007
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