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A098410
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Expansion of 1/(sqrt(1-4*x)*sqrt(1-8*x)).
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7
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1, 6, 38, 252, 1734, 12276, 88796, 652728, 4856902, 36478404, 275975028, 2099978568, 16054486044, 123213933576, 948713646072, 7325088811632, 56692748053062, 439689331938276, 3416328042565124, 26587566855421608
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Convolution of A000984(n) and 2^n*A000984(n). Convolution of A000984(n) and A059304. 4th binomial transform of A000984.
Largest coefficient of (1+6*x+x^2)^n . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 02 2007
Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the H steps can have 6 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 31 2008
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REFERENCES
| Francesc Fite, Kiran S. Kedlaya, Victor Rotger and Andrew V. Sutherland, Sato-Tate distributions and Galois endomorphism modules in genus 2, Arxiv preprint arXiv:1110.6638, 2011 (the sequence b_{6,n}).
Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
| G.f.: 1/sqrt(1-12*x+32*x^2).
E.g.f.: exp(6*x)*BesselI(0, 2*x).
a(n) = sum{k=0..n, 2^k*binomial(2*k, k)*binomial(2*(n-k), n-k)}.
a(n) = sum{k=0..n, C(n, k)*C(2*k, k)*4^(n-k)} - Paul Barry, Mar 08 2005
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CROSSREFS
| Sequence in context: A135030 A162558 A147957 * A079949 A026940 A082427
Adjacent sequences: A098407 A098408 A098409 * A098411 A098412 A098413
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 07 2004
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