From 68cdaa2c69269b466832f6331f41f11275466c21 Mon Sep 17 00:00:00 2001
From: John Benediktsson <mrjbq7@gmail.com>
Date: Tue, 9 Apr 2013 11:04:38 -0700
Subject: [PATCH] math.factorials: more factorial words.

---
 extra/math/factorials/factorials-tests.factor |  5 +++++
 extra/math/factorials/factorials.factor       | 12 +++++++++++-
 2 files changed, 16 insertions(+), 1 deletion(-)

diff --git a/extra/math/factorials/factorials-tests.factor b/extra/math/factorials/factorials-tests.factor
index 976bba91a0..8a94308e3e 100644
--- a/extra/math/factorials/factorials-tests.factor
+++ b/extra/math/factorials/factorials-tests.factor
@@ -60,3 +60,8 @@ IN: math.factorials
 { { 1 1 2 12 288 } } [ 5 iota [ super-factorial ] map ] unit-test
 
 { { 1 1 4 108 27648 } } [ 5 iota [ hyper-factorial ] map ] unit-test
+
+{ { 1 1 1 5 19 101 619 4421 35899 326981 } }
+[ 10 iota [ alternating-factorial ] map ] unit-test
+
+{ { 1 1 2 9 262144 } } [ 5 iota [ exponential-factorial ] map ] unit-test
diff --git a/extra/math/factorials/factorials.factor b/extra/math/factorials/factorials.factor
index 7964713c78..1f03a28456 100644
--- a/extra/math/factorials/factorials.factor
+++ b/extra/math/factorials/factorials.factor
@@ -1,7 +1,7 @@
 ! Copyright (C) 2013 John Benediktsson
 ! See http://factorcode.org/license.txt for BSD license
 
-USING: combinators kernel math math.functions math.primes
+USING: combinators fry kernel math math.functions math.primes
 math.ranges memoize sequences ;
 
 IN: math.factorials
@@ -91,3 +91,13 @@ ALIAS: pochhammer rising-factorial
     dup 1 > [
         [1,b] [ dup ^ ] [ * ] map-reduce
     ] [ drop 1 ] if ;
+
+: alternating-factorial ( n -- m )
+    dup 1 > [
+        [ [1,b] ] keep even? '[
+            [ factorial ] [ odd? _ = ] bi [ neg ] when
+        ] map-sum
+    ] [ drop 1 ] if ;
+
+: exponential-factorial ( n -- m )
+    dup 1 > [ [1,b] 1 [ swap ^ ] reduce ] [ drop 1 ] if ;