A130456 Triangle, read by rows of 2n+1 terms, where row n+1 is generated by taking partial sums of row n and then append a zero followed by the final term in the partial sums of row n, for n>=0, with T(0,0)=1.

1, 1, 0, 1, 1, 1, 2, 0, 2, 1, 2, 4, 4, 6, 0, 6, 1, 3, 7, 11, 17, 17, 23, 0, 23, 1, 4, 11, 22, 39, 56, 79, 79, 102, 0, 102, 1, 5, 16, 38, 77, 133, 212, 291, 393, 393, 495, 0, 495, 1, 6, 22, 60, 137, 270, 482, 773, 1166, 1559, 2054, 2054, 2549, 0, 2549, 1, 7, 29, 89, 226, 496, 978

Offset: 0

Author

Paul D. Hanna, May 26 2007

Keywords

• nonn
• tabf

Comments

Final term in row n equals A098746(n) = number of permutations of [1..n] which avoid 4231 and 42513.

Examples

			Triangle begins:
1;
1, 0, 1;
1, 1, 2, 0, 2;
1, 2, 4, 4, 6, 0, 6;
1, 3, 7, 11, 17, 17, 23, 0, 23;
1, 4, 11, 22, 39, 56, 79, 79, 102, 0, 102;
1, 5, 16, 38, 77, 133, 212, 291, 393, 393, 495, 0, 495;
1, 6, 22, 60, 137, 270, 482, 773, 1166, 1559, 2054, 2054, 2549, 0, 2549; ...
		

Crossrefs

Cf. A098746 (final term in rows).

Programs

PARI

{T(n,k)=local(A=[1],B);if(n==0,if(k==0,1,0),for(j=1,n, B=Vec(Ser(A)/(1-x));A=concat(concat(B,0),B[ #B]));A[k+1])}