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A270790 Multiplier of polynomial P_n(x) arising from RNA combinatorics.

%I A270790 #29 Apr 20 2016 11:46:58
%S A270790 1,21,11,143,88179,111435,111435,1361270295,1137235,9945637,
%T A270790 16009448637,19293438101,3607872924887,2630885818709841,
%U A270790 195084537038811,45500599374052095,1472444896343699846295,1997334750675075735,145805436799280528655,107268833547674677179
%N A270790 Multiplier of polynomial P_n(x) arising from RNA combinatorics.
%H A270790 Gheorghe Coserea, <a href="/A270790/b270790.txt">Table of n, a(n) for n = 1..100</a>
%H A270790 R. C. Penner, <a href="http://dx.doi.org/10.1090/bull/1524">Moduli Spaces and Macromolecules</a>, Bull. Amer. Math. Soc., 53 (2015), 217-268. See p. 259.
%F A270790 a(g) * P_g(0) = A035319(g) = (4*g-1)!!/(2*g+1), where P_g(x) is the polynomial associated with row g of the triangle A270791.
%o A270790 (PARI)
%o A270790 G = 20; N = 3*G + 1; F = 1; gmax(n) = min(n\2, G);
%o A270790 Q = matrix(N+1, G+1); Qn() = (matsize(Q)[1] - 1);
%o A270790 Qget(n, g) = { if (g < 0 || g > n/2, 0, Q[n+1, g+1]) };
%o A270790 Qset(n, g, v) = { Q[n+1, g+1] = v };
%o A270790 Quadric({x=1}) = {
%o A270790   Qset(0, 0, x);
%o A270790   for (n = 1, Qn(), for (g = 0, gmax(n),
%o A270790     my(t1 = (1+x)*(2*n-1)/3 * Qget(n-1, g),
%o A270790        t2 = (2*n-3)*(2*n-2)*(2*n-1)/12 * Qget(n-2, g-1),
%o A270790        t3 = 1/2 * sum(k = 1, n-1, sum(i = 0, g,
%o A270790        (2*k-1) * (2*(n-k)-1) * Qget(k-1, i) * Qget(n-k-1, g-i))));
%o A270790     Qset(n, g, (t1 + t2 + t3) * 6/(n+1))));
%o A270790 };
%o A270790 Quadric('x + O('x^(F+1)));
%o A270790 Kol(g) = vector(Qn()+2-F-2*g, n, polcoeff(Qget(n+F-2 + 2*g, g), F, 'x));
%o A270790 P(g) = {
%o A270790   my(x = 'x + O('x^(G+2)));
%o A270790   return(Pol(Ser(Kol(g)) * (1-4*x)^(3*g-1/2), 'x));
%o A270790 };
%o A270790 vector(G, g, content(P(g)))  \\ _Gheorghe Coserea_, Apr 17 2016
%Y A270790 Cf. A035309, A035319, A270791.
%K A270790 nonn,easy
%O A270790 1,2
%A A270790 _N. J. A. Sloane_, Mar 28 2016
%E A270790 More terms from _Gheorghe Coserea_, Apr 17 2016