OEIS/Infinite Products

Infinite Products in your CAS

A046042 Number of partitions of n into fourth powers.

• Maple

g := -1 + 1/product(1 - x^(j^4), j=1..10): 
gser := series(g, x=0, 105): seq(coeff(gser, x, n), n=1..102);

• Mathematica

g = -1 + 1/Product[1 - x^(j^4), {j, 1, 10}]; 
gser = Series[g, {x, 0, 105}]; Table[Coefficient[gser, x, n], {n, 1, 102}]

Generalized Euler transform

• defined by Seiichi Manyama in A266964

Product_{k>0} (1 - g(k)*x^k)^(- f(k)) = a(0) + a(1)*x + a(2)*x^2 + ...

1. If we set g(n) = 1, we get the usual Euler transform.
2. If we set f(n) = - h(n) and g(n) = -1, we get the weighout transform (cf. A026007).
3. If we set f(n) = - n (A001478) and g(n) = n (A000027), we get A266964.
4. With the default f(n) = g(n) = A000012 (all 1's), we get A000041 (number of partitions of n).