#1: " ----------[ D e r i v e ]---------- " User #2: " ---------- Initialization ---------- " User #3: " ---------- Combinatorial Theory ---------- " User User #4: " Pochhammer symbol (a)_n = a (a + 1) ... (a + n - 1) => a (a + 1) (a + 2) " #5: POCHHAMMER(a, 3) User #6: a*(a + 1)*(a + 2) Simp(#5) #7: " Binomial coefficient => n (n - 1) (n - 2)/6 " User #8: COMB(n, 3) User n*(n - 1)*(n - 2) #9: ------------------- Simp(#8) 6 #10: " 2^n n! (2 n - 1)!! => (2 n)! " User #11: "2^n * n! * (2*n - 1)!!" User #12: " 2^n n! product(2 k - 1, k = 1..n) => (2 n)! " User n n #13: 2 *n!*PRODUCT (2*k - 1) User k=1 2*n / 1 \ 2 *n!*|n - ---|! #14: \ 2 / Simp(#13) -------------------- SQRT(pi) User #15: " => (2 n)!/[2^(2 n) (n!)^2] or (2 n - 1)!!/[2^n n!] " / 1 \ GAMMA|n + ---| #16: \ 2 / User ---------------- SQRT(pi)*n! / 1 \ |n - ---|! #17: \ 2 / Simp(#16) ------------- SQRT(pi)*n! User #18: " Partitions of an integer => {1+1+1+1, 1+1+2, 1+3, 2+2, 4} (5 in all) " #19: 4 User #20: 4 Simp(#19) #21: " Stirling numbers of the first kind: S_1(5, 2) => -50 "User #22: "stirling1(5, 2)" User #23: " Euler's totient function => 576 " User #24: "totient(1776)" User #25: " ---------- Quit ---------- " User