A185676 Riordan array (((1+x)/(1-x-x^2))^m, x*A000108(x)), m=2.

1, 4, 1, 10, 5, 1, 22, 16, 6, 1, 45, 45, 23, 7, 1, 88, 121, 76, 31, 8, 1, 167, 325, 237, 116, 40, 9, 1, 310, 895, 728, 403, 166, 50, 10, 1, 566, 2563, 2253, 1358, 630, 227, 61, 11, 1, 1020, 7670, 7104, 4541, 2288, 930, 300, 73, 12, 1, 1819, 23939, 22919, 15249, 8145, 3604, 1316, 386, 86, 13, 1

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

1;
4,1;
10,5,1;
22,16,6,1;
45,45,23,7,1;
88,121,76,31,8,1;
167,325,237,116,40,9,1;
310,895,728,403,166,50,10,1;

Mathematica

r[n_, k_, m_] := k*Sum[ Sum[ Binomial[j-1, m-1]*Binomial[j, i+m-j], {j, m, i+m}]*Binomial[2*(n-i)-k-1, n-i-1]/(n-i), {i, 0, n-k}]; r[n_, 0, m_] := Sum[ Binomial[i-1, m-1]*Binomial[i, n+m-i], {i, m, n+m}]; Table[r[n, k, 2], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 21 2013 *)

Crossrefs

Column k=0 gives: A004798(n+1).

Sequence in context: A104713 A185945 A186368 * A277583 A213765 A349809

Adjacent sequences: A185673 A185674 A185675 * A185677 A185678 A185679

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 09 2011

Status

approved