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A096815 Triangle, read by rows, such that T(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and k. 5
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 4, 4, 1, 1, 1, 5, 6, 7, 5, 1, 1, 1, 6, 9, 11, 9, 6, 1, 1, 1, 7, 11, 17, 17, 13, 7, 1, 1, 1, 8, 14, 24, 30, 26, 16, 8, 1, 1, 1, 9, 18, 32, 42, 50, 36, 21, 9, 1, 1, 1, 10, 21, 42, 61, 79, 76, 51, 25, 10, 1, 1, 1, 11, 25, 53, 85, 118, 129, 115, 67 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Row sums are A096816.

LINKS

Table of n, a(n) for n=0..87.

FORMULA

T(n, k) = Sum_{j=0..min(n-k, k)} T(n-k, j)*T(k, k-j), for n>=k>=1, with T(n, 0)=T(n+1, 1)=T(n, n)=1 for n>=0.

EXAMPLE

T(7,4) = 11 = 4th term of the convolution of row (7-4) and row 4:

T(3,0)*T(4,4) + T(3,1)*T(4,3) + T(3,2)*T(4,2) + T(3,3)*T(4,1).

Rows begin:

[1],

[1,1],

[1,1,1],

[1,1,2,1],

[1,1,3,3,1],

[1,1,4,4,4,1],

[1,1,5,6,7,5,1],

[1,1,6,9,11,9,6,1],

[1,1,7,11,17,17,13,7,1],

[1,1,8,14,24,30,26,16,8,1],

[1,1,9,18,32,42,50,36,21,9,1],

[1,1,10,21,42,61,79,76,51,25,10,1],

[1,1,11,25,53,85,118,129,115,67,31,11,1],...

PROG

(PARI) T(n, k)=if(n<k || k<0, 0, if(k<=1 || k==n, 1, sum(j=0, k, T(n-k, j)*T(k, k-j))))

(Maxima) T(n, k):= if ( n<k or k<0 ) then 0 else

if ( k<=1 or k=n ) then 1 else sum(T(n-k, j)*T(k, k-j), j, 0, k);

create_list(T(n, k), n, 0, 12, k, 0, n); /* Emanuele Munarini, May 12 2012 */

CROSSREFS

Cf. A096816, A096811.

Sequence in context: A136043 A336420 A254055 * A193516 A124445 A124279

Adjacent sequences:  A096812 A096813 A096814 * A096816 A096817 A096818

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 20 2004

STATUS

approved

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Last modified April 13 19:42 EDT 2021. Contains 342941 sequences. (Running on oeis4.)