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 A158823 Triangle read by rows: matrix product A004736 * A158821. 4

%I

%S 1,3,1,6,2,2,10,3,4,3,15,4,6,6,4,21,5,8,9,8,5,28,6,10,12,12,10,6,36,7,

%T 12,15,16,15,12,7,45,8,14,18,20,20,18,14,8,55,9,16,21,24,25,24,21,16,

%U 9,66,10,18,24,28,30,30,28,24,18,10,78,11,20,27,32,35,36,35,32,27,20,11

%N Triangle read by rows: matrix product A004736 * A158821.

%H G. C. Greubel, <a href="/A158823/b158823.txt">Rows n = 1..50 of the triangle, flattened</a>

%F Sum_{k=1..n} T(n, k) = A000292(n).

%F T(n, k) = Sum_{j=k..n} A004736(n, j)*A158821(j-1, k-1).

%F From _R. J. Mathar_, Mar 03 2011: (Start)

%F T(n, k) = (n-k+1)*(k-1), k>1.

%F T(n, 1) = A000217(n). (End)

%e First few rows of the triangle =

%e 1;

%e 3, 1;

%e 6, 2, 2;

%e 10, 3, 4, 3;

%e 15, 4, 6, 6, 4;

%e 21, 5, 8, 9, 8, 5;

%e 28, 6, 10, 12, 12, 10, 6;

%e 36, 7, 12, 15, 16, 15, 12, 7;

%e 45, 8, 14, 18, 20, 20, 18, 14, 8;

%e 55, 9, 16, 21, 24, 25, 24, 21, 16, 9;

%e 66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10;

%e 78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11;

%e 91, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12;

%p A158823 := proc(n,m) add( A004736(n,k)*A158821(k-1,m-1),k=1..n) ; end: seq(seq(A158823(n,m),m=1..n),n=1..8) ; # _R. J. Mathar_, Oct 22 2009

%t Table[If[k==1, Binomial[n+1, 2], (n-k+1)*(k-1)], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 01 2021 *)

%o (Magma) [k eq 1 select Binomial(n+1, 2) else (n-k+1)*(k-1): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 01 2021

%o (Sage) flatten([[binomial(n+1, 2) if k==1 else (n-k+1)*(k-1) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Apr 01 2021

%Y Cf. A000292 (row sums), A003991, A004736, A158821.

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_ & _Roger L. Bagula_, Mar 28 2009

%E Corrected A-number in a formula - _R. J. Mathar_, Oct 30 2009

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Last modified May 12 02:06 EDT 2021. Contains 343808 sequences. (Running on oeis4.)