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

0,7

Comments

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

Links

Table of n, a(n) for n=0..70.

Example

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; ...

Prog

(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])}

Crossrefs

Cf. A098746 (final term in rows).

Sequence in context: A206298 A076608 A068461 * A222049 A071497 A125939

Adjacent sequences: A130453 A130454 A130455 * A130457 A130458 A130459

Keyword

nonn,tabf

Author

Paul D. Hanna, May 26 2007

Status

approved