A185664 Riordan array (A000045(x)^m,x*A000108(x)), m=3.

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, 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, 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

Offset: 0

Author

Vladimir Kruchinin, Feb 08 2011

Keywords

• nonn
• tabl

Examples

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

Links

• Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Crossrefs

Cf. A001628 (column k=0).

Formula

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.

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.