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A084601
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Coefficients of 1/(1-2x-7x^2)^(1/2); also, a(n) is the central coefficient of (1+x+2x^2)^n.
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9
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1, 1, 5, 13, 49, 161, 581, 2045, 7393, 26689, 97285, 355565, 1305745, 4808545, 17760965, 65753693, 243954113, 906758785, 3375949829, 12587460557, 46995614449, 175669746209, 657370655045, 2462383495357, 9232029156001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The Hankel transform (see A001906 for definition) of this sequence is A036442 : 1, 4, 32, 512, 16384, ... . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 03 2005
Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), U (or D) can have 2 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Feb 05 2008
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REFERENCES
| 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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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..120
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FORMULA
| E.g.f.: exp(x)*BesselI(0, 2*sqrt(2)*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 21 2004
a(n)=sum{k=0..floor(n/2), binomial(n-k, k)binomial(n, k)2^k}. - Paul Barry (pbarry(AT)wit.ie), Aug 26 2004
Sum[k=0..n, Trinomial(k, n) Binomial(n, k) ], with Trinomial=A027907. - R. Stephan, Jan 28 2005
a(n) is also the central coefficient of (2+x+x^2)^n; a(n)=sum_{k=0..n} C(n,k) T(k,n), where T(k,n) is the triangle of trinomial coefficients = coefficient of x^n of (1+x+x^2)^k : A027907 - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Feb 05 2008
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MATHEMATICA
| CoefficientList[Series[1/Sqrt[1-2x-7x^2], {x, 0, 30}], x] (* From Harvey P. Dale, Sep 18 2011 *)
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PROG
| (PARI) for(n=0, 30, t=polcoeff((1+x+2*x^2)^n, n, x); print1(t", "))
(Maxima) a(n):=coeff(expand((1+x+2*x^2)^n), x, n);
makelist(a(n), n, 0, 12); /* Emanuele Munarini, Mar 02 2011 */
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CROSSREFS
| Cf. A002426, A084600, A084602-A084615.
Sequence in context: A146152 A082132 A138277 * A149532 A149533 A149534
Adjacent sequences: A084598 A084599 A084600 * A084602 A084603 A084604
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 01 2003
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