A249794 - OEIS

%I #5 Nov 12 2014 21:29:48

%S 1,1,8,44,232,1253,6895,38376,215396,1217109,6914696,39458777,

%T 226006814,1298557455,7481167001,43200760775,249977853797,

%U 1449092483085,8413731049376,48922225054030,284830701327470,1660264158620798,9687938318036091,56586034949700662

%N G.f.: Sum_{n>=0} x^n/(1-x)^(6*n) * Sum_{k=0..n} C(n,k)^2 * x^k.

%F G.f.: (1-x)^5 / sqrt((1 - 3*x + x^2)*(1 - x + 2*x^2 - x^3)*(1 - 8*x + 14*x^2 - 12*x^3 + 5*x^4 - x^5)).

%F G.f.: (1-x)^5 / sqrt(1 - 12*x + 52*x^2 - 124*x^3 + 206*x^4 - 246*x^5 + 208*x^6 - 120*x^7 + 45*x^8 - 10*x^9 + x^10).

%e G.f.: A(x) = 1 + x + 8*x^2 + 44*x^3 + 232*x^4 + 1253*x^5 + 6895*x^6 +...

%e where

%e A(x) = 1 + x/(1-x)^6*(1+x) + x^2/(1-x)^12*(1+2^2*x+x^2) + x^3/(1-x)^18*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^24*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^30*(1+5^2*x+10^2*x^2+10^2*x^3+5^2*x^4+x^5) +...

%o (PARI) {a(n)=polcoeff( sum(m=0, n, x^m * sum(k=0, m, binomial(m, k)^2 * x^k) / (1-x +x*O(x^n))^(6*m)), n)}

%o for(n=0, 30, print1(a(n), ", "))

%o (PARI) {a(n)=polcoeff( (1-x)^5 / sqrt((1 - 3*x + x^2)*(1 - x + 2*x^2 - x^3)*(1 - 8*x + 14*x^2 - 12*x^3 + 5*x^4 - x^5) +x*O(x^n)), n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A249946, A249792, A249793.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 12 2014