A208890 - OEIS

%I #5 Mar 30 2012 18:37:37

%S 1,4,60,1200,27300,668304,17153136,455083200,12372574500,342766138000,

%T 9638583800560,274341178587840,7887308884400400,228685287180840000,

%U 6678543795015960000,196260140322869011200,5798873833602270315300,172160337343624495866000

%N  a(n) = A000984(n)*A004981(n), the term-wise product of the coefficients in (1-4*x)^(-1/2) and (1-8*x)^(-1/4).

%C  The sequences A000984 and A004981 are related by the aesthetic identity:

%C Sum_{n>=0} A000984(n)^3 *x^n = ( Sum_{n>=0} A004981(n)^2 *x^n )^2.

%e  G.f.: A(x) = 1 + 4*x + 60*x^2 + 1200*x^3 + 27300*x^4 + 668304*x^5 +...

%e The terms are the term-wise products of the sequences:

%e A000984 = [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...],

%e A004981 = [1, 2, 10, 60, 390, 2652, 18564, 132600, 961350, ...].

%e Related sequences:

%e A^2: [1, 8, 136, 2880, 67800, 1699008, 44368704, 1193107968, ...],

%e A^4: [1, 16, 336, 7936, 200176, 5266176, 142657536, 3948773376, ...],

%e A^8: [1, 32, 928, 26624, 767200, 22270976, 651331072, 19178651648, ...].

%o  (PARI) {A000984(n)=polcoeff((1-4*x +x*O(x^n))^(-1/2),n)}

%o {A004981(n)=polcoeff((1-8*x +x*O(x^n))^(-1/4),n)}

%o {a(n)=A000984(n)*A004981(n)}

%o for(n=0,20,print1(a(n),", "))

%Y  Cf. A000984, A004981, A181418.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 04 2012