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A081671
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Expansion of exp(4x)I_0(2x).
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10
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1, 4, 18, 88, 454, 2424, 13236, 73392, 411462, 2325976, 13233628, 75682512, 434662684, 2505229744, 14482673832, 83940771168, 487610895942, 2838118247064, 16547996212044, 96635257790352, 565107853947444
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A026375. Second binomial transform of A000984.
Largest coefficient of (1+4x+x^2)^n. - Paul Barry (pbarry(AT)wit.ie), Dec 15 2003
Row sums of triangle in A124574 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 27 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 come in 4 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Feb 05 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
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
| a(n) = sum{m=0..n, sum{k=0..m, C(n, m)C(m, k)C(2k, k)}}
G.f.: 1/sqrt((1-2*x)*(1-6*x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 09 2003
a(n)=sum{k=0..n, 2^(n-k)*C(n, k)C(2k, k)} - Paul Barry (pbarry(AT)wit.ie), Jan 27 2005
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CROSSREFS
| Sequence in context: A083325 A050146 A083879 * A006629 A068764 A127394
Adjacent sequences: A081668 A081669 A081670 * A081672 A081673 A081674
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 28 2003
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