A091702 -id:A091702 - cp's OEIS frontend

A091700 Matrix square of triangle A063967.

1, 2, 1, 7, 6, 1, 23, 29, 10, 1, 78, 127, 67, 14, 1, 264, 527, 375, 121, 18, 1, 895, 2113, 1892, 831, 191, 22, 1, 3034, 8269, 8922, 4973, 1559, 277, 26, 1, 10286, 31781, 40115, 27139, 10826, 2623, 379, 30, 1, 34872, 120448, 174080, 138617, 67308, 20763, 4087, 497, 34, 1

Offset: 0

Christian G. Bower, Jan 29 2004

			   1;
   2,   1;
   7,   6,  1;
  23,  29, 10,  1;
  78, 127, 67, 14, 1;
  ...

Row sums: A091701.

Column 0: A091702.

A112973 Riordan array (1/(1-x-x^2), x(1+x)/(1-x-x^2)^2).

Original entry on oeis.org

1, 1, 1, 2, 4, 1, 3, 12, 7, 1, 5, 31, 31, 10, 1, 8, 73, 110, 59, 13, 1, 13, 162, 340, 267, 96, 16, 1, 21, 344, 956, 1022, 529, 142, 19, 1, 34, 707, 2507, 3479, 2416, 923, 197, 22, 1, 55, 1416, 6231, 10850, 9657, 4900, 1476, 261, 25, 1, 89, 2778, 14840, 31606, 34905

Offset: 0

Paul Barry, Oct 07 2005

Row sums are A091702. Diagonal sums are A052960. First column is A000045(n+1).

Second column is A129707. - Ralf Stephan, Dec 31 2013

			Rows begin
1;
1,1;
2,4,1;
3,12,7,1;
5,31,31,10,1;
8,73,110,59,13,1;

T(n,k):=sum(binomial(m,n-m)*binomial(m+k,2*k),m,floor(n/2),n); /* Vladimir Kruchinin, Apr 21 2015 */

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) - 2*T(n-3,k) - T(n-4,k), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 4, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 21 2014
G.f.: (x^2+x-1)/((x^2+x)*y-x^4-2*x^3+x^2+2*x-1). - Vladimir Kruchinin, Apr 21 2015
T(n,k) = Sum_{m=floor(n/2)..n} C(m,n-m)*C(m+k,2*k). - Vladimir Kruchinin, Apr 21 2015

Definition corrected by Ralf Stephan, Dec 31 2013

cp's OEIS Frontend

A091700 Matrix square of triangle A063967.

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A112973 Riordan array (1/(1-x-x^2), x(1+x)/(1-x-x^2)^2).

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