A115080 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A115080

Triangle, read by rows, where T(n,k) equals the dot product of the vector of terms in row n that are to the right of T(n,k) with the vector of terms in column k that are above T(n,k): T(n,k) = Sum_{j=0..n-k-1} T(n,j+k+1)*T(j+k,k) for n > k+1 > 0, with T(n,n) = 1 and T(n,n-1) = n (n>=1).

1, 1, 1, 3, 2, 1, 11, 5, 3, 1, 50, 20, 7, 4, 1, 257, 94, 31, 9, 5, 1, 1467, 507, 150, 44, 11, 6, 1, 9081, 3009, 853, 218, 59, 13, 7, 1, 60272, 19350, 5251, 1307, 298, 76, 15, 8, 1, 424514, 132920, 35109, 8313, 1881, 390, 95, 17, 9, 1, 3151226, 966962, 249332

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Triangle A115085 is the dual of this triangle.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..350, as a flattened triangle of rows 0..25.

EXAMPLE

T(n,k) = [T(n,k+1),T(n,k+2),...,T(n,n)]*[T(k,k),T(k+1,k),...,T(n-1,k)]:

T(3,0) = [5,3,1]*[1,1,3] = 5*1 + 3*1 + 1*3 = 11;

T(4,1) = [7,4,1]*[1,2,5] = 7*1 + 4*2 + 1*5 = 20;

T(5,1) = [31,9,5,1]*[1,2,5,20] = 31*1 + 9*2 + 5*5 + 1*20 = 94;

T(6,2) = [44,11,6,1]*[1,3,7,31] = 44*1 + 11*3 + 6*7 + 1*31 = 150.

Triangle begins:

1, 1;

3, 2, 1;

11, 5, 3, 1;

50, 20, 7, 4, 1;

257, 94, 31, 9, 5, 1;

1467, 507, 150, 44, 11, 6, 1;

9081, 3009, 853, 218, 59, 13, 7, 1;

60272, 19350, 5251, 1307, 298, 76, 15, 8, 1;

424514, 132920, 35109, 8313, 1881, 390, 95, 17, 9, 1;

3151226, 966962, 249332, 57738, 12315, 2587, 494, 116, 19, 10, 1;

24510411, 7396366, 1873214, 422948, 88737, 17377, 3437, 610, 139, 21, 11, 1;

...

PROG

(PARI) {T(n, k)=if(n==k, 1, if(n==k+1, n, sum(j=0, n-k-1, T(n, j+k+1)*T(j+k, k))))}

for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A115081 (column 0), A115082 (column 1), A115083 (column 2), A115084 (row sums); A115085 (dual triangle).

Sequence in context: A325305 A309951 A077756 * A222730 A104219 A123513

Adjacent sequences: A115077 A115078 A115079 * A115081 A115082 A115083

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jan 13 2006

STATUS

approved