|
%I #7 Nov 12 2014 21:23:04
%S 1,1,7,35,171,856,4359,22446,116557,609289,3202088,16902558,89550391,
%T 475922764,2536113322,13545996260,72500109601,388730700761,
%U 2087639484747,11227578293407,60461487361452,325972272495485,1759323533735344,9504604121313715,51393787321667969,278127959744155754
%N G.f.: Sum_{n>=0} x^n/(1-x)^(5*n) * Sum_{k=0..n} C(n,k)^2 * x^k.
%F G.f.: (1-x)^4 / sqrt(1 - 10*x + 33*x^2 - 56*x^3 + 66*x^4 - 54*x^5 + 28*x^6 - 8*x^7 + x^8).
%e G.f.: A(x) = 1 + x + 7*x^2 + 35*x^3 + 171*x^4 + 856*x^5 + 4359*x^6 +...
%e where
%e A(x) = 1 + x/(1-x)^5*(1+x) + x^2/(1-x)^10*(1+2^2*x+x^2) + x^3/(1-x)^15*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^20*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^25*(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))^(5*m)), n)}
%o for(n=0, 30, print1(a(n), ", "))
%o (PARI) {a(n)=polcoeff( (1-x)^5 / sqrt(1 - 10*x + 33*x^2 - 56*x^3 + 66*x^4 - 54*x^5 + 28*x^6 - 8*x^7 + x^8 +x*O(x^n)), n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A249946, A249792, A249794.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 12 2014
|
