A130454 Triangle, read by rows of (n+1)(n+2)/2 terms, where row n+1 is generated by taking partial sums of row n and then appending n+1 zeros followed by the final term in the partial sums of row n for n>=0.

1, 1, 0, 1, 1, 1, 2, 0, 0, 2, 1, 2, 4, 4, 4, 6, 0, 0, 0, 6, 1, 3, 7, 11, 15, 21, 21, 21, 21, 27, 0, 0, 0, 0, 27, 1, 4, 11, 22, 37, 58, 79, 100, 121, 148, 148, 148, 148, 148, 175, 0, 0, 0, 0, 0, 175, 1, 5, 16, 38, 75, 133, 212, 312, 433, 581, 729, 877, 1025, 1173, 1348, 1348, 1348

Offset

0,7

Links

Table of n, a(n) for n=0..72.

Example

Triangle begins:
.1;
.1, 0, 1;
.1, 1, 2, 0,0, 2;
.1, 2, 4, 4, 4, 6, 0,0,0, 6;
.1, 3, 7,11,15,21,21, 21, 21, 27, 0,0,0,0, 27;
.1, 4,11,22,37,58,79,100,121,148,148,148,148,148,175, 0,0,0,0,0, 175; ...

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, vector(j)), B[ #B])); A[k+1])}

Crossrefs

Cf. A130455 (final term in rows).

Sequence in context: A341023 A241067 A130457 * A070787 A033985 A216218

Adjacent sequences: A130451 A130452 A130453 * A130455 A130456 A130457

Keyword

nonn,tabf

Author

Paul D. Hanna, May 26 2007

Extensions

Changed keyword tabl to tabf - R. J. Mathar, Mar 30 2010

Status

approved