Problem Statement

Pascal's triangle is an arithmetic and geometric figure often associated with the name of Blaise Pascal, but also studied centuries earlier in India, Persia, China and elsewhere. Its first few rows look like this: where each element of each row is either 1 or the sum of the two elements right above it. For example, the next row of the triangle would be: So the triangle now looks like this: Each row   n   (starting with row   0   at the top) shows the coefficients of the binomial expansion of   (x + y)n.

Write a function that prints out the first   n   rows of the triangle   (with   f(1)   yielding the row consisting of only the element 1). This can be done either by summing elements from the previous rows or using a binary coefficient or combination function. Behavior for   n ≤ 0   does not need to be uniform, but should be noted.

Let's start with the solution:

PASCAL
=LAMBDA(n,
    BINCOEFF(n - 1)(
        SEQUENCE(1, n, 0, 1)
    )
)


BINCOEFF
=LAMBDA(n,
    LAMBDA(k,
        QUOTIENT(FACT(n), FACT(k) * FACT(n - k))
    )
)


TRIANGLE
=LAMBDA(n,
    LET(
        ixs, SEQUENCE(n, n, 0, 1),
        x, MOD(ixs, n),
        y, QUOTIENT(ixs, n),
        IF(x <= y,
            BINCOEFF(y)(x),
            ""
        )
    )
)