login
a(1)=1; thereafter a(n) = (n/2)*Sum_{i=1..n-1} K(i,n-i)*a(i)*a(n-i), where K(i,j)=i/j+j/i+2.
0

%I #10 Dec 06 2017 03:43:29

%S 1,4,54,1280,44500,2095632,127881376,9819500544,928097190000,

%T 106056995000000,14432021983025504,2308065337772034048,

%U 428863163196474895616,91656939861553564825600,22332165732277725605760000,6154560612828089005182025728,1905106896258617768240402396928,658221263587332244069472967367680,252407458471654722567803941053452800

%N a(1)=1; thereafter a(n) = (n/2)*Sum_{i=1..n-1} K(i,n-i)*a(i)*a(n-i), where K(i,j)=i/j+j/i+2.

%H P. L. Krapivsky and Colm Connaughton, <a href="http://arxiv.org/abs/1203.3905">Driven Brownian coagulation of polymers</a>, arXiv preprint arXiv:1203.3905, 2012

%p K:=(i,j)->i/j+j/i+2;

%p B:=proc(n) option remember; global K;

%p if n=1 then 1 else

%p (n/2)*add( K(i,n-i)*B(i)*B(n-i), i=1..n-1); fi; end;

%t K[i_, j_] := i/j + j/i + 2;

%t a[1] = 1; a[n_] := a[n] = (n/2) Sum[K[i, n-i] a[i] a[n-i], {i, 1, n-1}];

%t Array[a, 19] (* _Jean-François Alcover_, Dec 06 2017 *)

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Sep 17 2012