A075473 n^n + n! - 2*(n+1)^(n-1).

0, 0, 0, 1, 30, 653, 13762, 304295, 7251598, 187783369, 5287733418, 161516858963, 5332258661782, 189493508862461, 7219703867130466, 293780009979371503, 12721918893479808030, 584361555380576356625, 28385640762100638931546

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.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) =A000312(n)+A000142(n)-2*A000272(n+1)

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

Sequence in context: A136661 A264849 A111779 * A051563 A152499 A027475

Adjacent sequences: A075470 A075471 A075472 * A075474 A075475 A075476

Keyword

nonn

Author

Henry Bottomley, Oct 11 2002

Status

approved