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A098409
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Expansion of 1/(sqrt(1-3x)sqrt(1-7x)).
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6
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1, 5, 27, 155, 931, 5775, 36645, 236325, 1542195, 10153775, 67313377, 448691985, 3004182349, 20188647185, 136094684907, 919884469275, 6232016686995, 42305974804575, 287706424085745, 1959685788407025, 13367193276457881
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A081671. 3rd binomial transform of A000984. Binomial transform is A098410.
Largest coefficient of (1+5*x+x^2)^n ; row sums of triangle in A126331 . - 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 come in five colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Feb 05 2008
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 five 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_{5,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(1-10x+21x^2); E.g.f.: exp(5x)BesselI(0, 2x).
a(n)=sum{k=0..n, C(n, k)C(2k, k)3^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Mar 08 2005
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CROSSREFS
| Sequence in context: A184702 A083326 A083880 * A052227 A101386 A153233
Adjacent sequences: A098406 A098407 A098408 * A098410 A098411 A098412
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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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