Expansion of polynomials

• A295237 a:=series(csc(x)*(1-sqrt(1-4*sin(x)))/2, x=0, 20): seq(n!*coeff(a, x, n), n=0..19); # E.g.f.
• A345969 Expansion of the e.g.f. 1 / sqrt(3 - 2 / ((1 - x)*exp(x))). Maple: a := series(1/sqrt(3-2/((1-x)*exp(x))), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); jOEIS: new PolynomialFieldSequence(0, "[[1],[1,-1]]" ",1,3,2,p1,x,exp,*,/,-,sqrt,/", 0, 1)

Postfix notation

The expansion of (exponential) generating functions is performed by PolynomialFieldSequence with a constructor that has up to 5 parameters:

• offset: first index
• polys: a list of list of integers in square brackets, specifying the coefficients of a list of polynomials. The polynomials are referenced by p0, p1, p2, ... where p0 gives the initial term of the iteration. For example, 1-x = 1*x^0 -1*x^1 -> [1,-1].
• postfix: a string starting with a delimiter, followed by a list of elements that are separated by this delimiter
• dist: an optional increment to the current index
• gfType: 0 for an o.g.f., 1 for an e.g.f., +4 if the denominator should be returned instead of the numerator (default 0 = o.g.f)
• modulus, factor: which element to take when zeros are suppressed (default 1), and periodicity when zeroes are suppressed (default 1). Even coefficients are selected by (0,2), odd coefficients by (1,2).