A208890 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).

1, 4, 60, 1200, 27300, 668304, 17153136, 455083200, 12372574500, 342766138000, 9638583800560, 274341178587840, 7887308884400400, 228685287180840000, 6678543795015960000, 196260140322869011200, 5798873833602270315300, 172160337343624495866000

Offset

0,2

Comments

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

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

Links

Table of n, a(n) for n=0..17.

Example

 G.f.: A(x) = 1 + 4*x + 60*x^2 + 1200*x^3 + 27300*x^4 + 668304*x^5 +...
The terms are the term-wise products of the sequences:
A000984 = [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...],
A004981 = [1, 2, 10, 60, 390, 2652, 18564, 132600, 961350, ...].
Related sequences:
A^2: [1, 8, 136, 2880, 67800, 1699008, 44368704, 1193107968, ...],
A^4: [1, 16, 336, 7936, 200176, 5266176, 142657536, 3948773376, ...],
A^8: [1, 32, 928, 26624, 767200, 22270976, 651331072, 19178651648, ...].

Prog

 (PARI) {A000984(n)=polcoeff((1-4*x +x*O(x^n))^(-1/2), n)}
{A004981(n)=polcoeff((1-8*x +x*O(x^n))^(-1/4), n)}
{a(n)=A000984(n)*A004981(n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A000984, A004981, A181418.

Sequence in context: A227528 A156090 A181418 * A370498 A325154 A013486

Adjacent sequences: A208887 A208888 A208889 * A208891 A208892 A208893

Keyword

nonn

Author

Paul D. Hanna, Mar 04 2012

Status

approved