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 A122177 Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 2, n-k) for n>=k>=0. 5

%I

%S 1,3,1,6,4,1,10,10,6,1,15,20,21,9,1,21,35,56,45,13,1,28,56,126,165,91,

%T 18,1,36,84,252,495,455,171,24,1,45,120,462,1287,1820,1140,300,31,1,

%U 55,165,792,3003,6188,5985,2600,496,39,1,66,220,1287,6435,18564,26334

%N Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 2, n-k) for n>=k>=0.

%C Remarkably, column k of the matrix inverse (A121437) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 3) for k>=0.

%e Triangle begins:

%e 1;

%e 3, 1;

%e 6, 4, 1;

%e 10, 10, 6, 1;

%e 15, 20, 21, 9, 1;

%e 21, 35, 56, 45, 13, 1;

%e 28, 56, 126, 165, 91, 18, 1;

%e 36, 84, 252, 495, 455, 171, 24, 1;

%e 45, 120, 462, 1287, 1820, 1140, 300, 31, 1; ...

%o (PARI) T(n,k)=if(n<k|k<0,0,binomial(k*(k+1)/2+n-k+2,n-k))

%Y Cf. A121437 (inverse); variants: A098568, A122175, A122176.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Aug 25 2006

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Last modified June 18 13:35 EDT 2021. Contains 345112 sequences. (Running on oeis4.)