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A132784 Triangle, read by rows of n*(n+1)/2 + 1 terms, where row n begins with n zeros followed by reverse partial sums of the prior row. 2
1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 2, 4, 6, 7, 7, 7, 7, 0, 0, 0, 0, 0, 7, 14, 21, 28, 34, 38, 40, 40, 40, 40, 40, 0, 0, 0, 0, 0, 0, 40, 80, 120, 160, 200, 238, 272, 300, 321, 335, 342, 342, 342, 342, 342, 342, 0, 0, 0, 0, 0, 0, 0, 342, 684, 1026, 1368, 1710, 2052, 2387 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Main diagonal (A132785) also yields (with offset) the row sums and the rightmost border of this triangle.

LINKS

Table of n, a(n) for n=0..76.

EXAMPLE

Triangle begins:

1;

0, 1;

0,0, 1,1;

0,0,0, 1,2,2,2;

0,0,0,0, 2,4,6,7,7,7,7;

0,0,0,0,0, 7,14,21,28,34,38,40,40,40,40,40;

0,0,0,0,0,0, 40,80,120,160,200,238,272,300,321,335,342,342,342,342,342,342; ...

To obtain row 4 from row 3: [0,0,0, 1,2,2,2], start with 4 zeros followed by the partial sums of the reverse of row 3: partial_sums([2,2,2,1, 0,0,0]) = [2,4,6,7, 7,7,7].

PROG

(PARI) {T(n, k)=local(A=[1]); if(n==0, 1, for(i=1, n, B=Vec(Pol(A)/(1-x +x*O(x^(i*(i-1)/2)))); A=concat(vector(i), B)); A[k+1])}

CROSSREFS

Cf. A132785 (main diagonal), A132786 (column sums).

Sequence in context: A093315 A204267 A237452 * A180834 A214458 A133873

Adjacent sequences:  A132781 A132782 A132783 * A132785 A132786 A132787

KEYWORD

nonn,tabf

AUTHOR

Paul D. Hanna, Aug 29 2007

STATUS

approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)