A185664 - OEIS

%I #18 Oct 30 2022 10:03:20

%S 0,0,0,0,0,0,1,0,0,0,3,1,0,0,0,9,4,1,0,0,0,22,14,5,1,0,0,0,51,42,20,6,

%T 1,0,0,0,111,120,69,27,7,1,0,0,0,233,335,224,104,35,8,1,0,0,0,474,940,

%U 707,372,148,44,9,1,0,0,0,942,2695,2221,1281,574,202,54,10,1,0,0,0,1836,7980,7038,4343,2122,841,267,65,11,1,0,0,0

%N Riordan array (A000045(x)^m,x*A000108(x)), m=3.

%H Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

%F R(n,k,m)=k*sum(i=0..n-k, sum(j=ceiling((i-m)/2)..i-m, binomial(j,i-m-j)*binomial(m+j-1,m-1))*binomial(2*(n-i)-k-1,n-i-1)/(n-i)), k>0.

%F R(n,0,m)=sum(j=ceiling((i-m)/2)..n-m, binomial(j,n-m-j)*binomial(m+j-1,m-1)), m=3.

%e 0;

%e 0,0;

%e 0,0,0;

%e 1,0,0,0;

%e 3,1,0,0,0;

%e 9,4,1,0,0,0;

%e 22,14,5,1,0,0,0;

%e 51,42,20,6,1,0,0,0;

%Y Cf. A001628 (column k=0).

%K nonn,tabl

%O 0,11

%A _Vladimir Kruchinin_, Feb 08 2011