OFFSET
0,5
COMMENTS
Possibly the number of patterns for forming an ordered sum of n values v1+v2+...+vn chosen (possibly with repetition) from {b1,b2,...,bn} with b1<b2<...<bn, where the question of whether v1+v2+...+vn is greater than, less than or equal to b1+b2+...+bn depends of the values of {b1,b2,...,bn}: for example with n=3 b2+b2+b2 is not immediately clear, while with n=4 there are 30 unclear possibilities namely b2+b2+b2+b2, b3+b3+b3+b3, 6 permutations of b1+b1+b4+b4, 6 permutations of b2+b2+b3+b3, 4 permutations of b2+b2+b2+b3, 4 permutations of b2+b3+b3+b3, 4 permutations of b2+b2+b2+b4 and 4 permutations of b1+b3+b3+b3.
EXAMPLE
a(2)=2^2+2!-2*3^1=4+2-6=0. a(3)=3^3+3!-2*4^2=27+6-32=1. a(4)=4^4+4!-2*5^3=256+24-250=30.
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 11 2002
STATUS
approved