

A075473


n^n + n!  2*(n+1)^(n1).


4



0, 0, 0, 1, 30, 653, 13762, 304295, 7251598, 187783369, 5287733418, 161516858963, 5332258661782, 189493508862461, 7219703867130466, 293780009979371503, 12721918893479808030, 584361555380576356625, 28385640762100638931546
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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+26=0. a(3)=3^3+3!2*4^2=27+632=1. a(4)=4^4+4!2*5^3=256+24250=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



