|
%I #27 Feb 16 2022 11:04:09
%S 1,4,2,6,6,3,8,12,12,4,10,20,30,20,5,12,30,60,60,30,6,14,42,105,140,
%T 105,42,7,16,56,168,280,280,168,56,8,18,72,252,504,630,504,252,72,9,
%U 20,90,360,840,1260,1260,840,360,90,10
%N A103516 * A007318 as an infinite lower triangular matrix.
%H G. C. Greubel, <a href="/A135853/b135853.txt">Table of n, a(n) for the first 50 rows</a>
%F T(n, k) = (A103516 * A007318)(n, k).
%F Sum_{k=0..n} T(n, k) = A135854(n).
%F T(n, k) = (k+1)*binomial(n+1, k+1), with T(n, n) = n+1, T(n, 0) = 2*(n+1). - _G. C. Greubel_, Dec 07 2016
%F T(n, 0) = A103517(n). - _G. C. Greubel_, Feb 06 2022
%e First few rows of the triangle are:
%e 1;
%e 4, 2;
%e 6, 6, 3;
%e 8, 12, 12, 4;
%e 10, 20, 30, 20, 5;
%e 12, 30, 60, 60, 30, 6;
%e 14, 42, 105, 140, 105, 42, 7;
%e ...
%t T[n_, k_]:= If[k==n, n+1, If[k==0, 2*(n+1), (k+1)*Binomial[n+1, k+1]]];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//flatten (* _G. C. Greubel_, Dec 07 2016 *)
%o (Sage)
%o def A135853(n,k):
%o if (n==0): return 1
%o elif (k==0): return 2*(n+1)
%o else: return (k+1)*binomial(n+1, k+1)
%o flatten([[A135853(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Feb 06 2022
%Y Cf. A007318, A103516.
%Y Cf. A103517 (1st column), A135854 (row sums).
%Y Cf. A135852 (= A007318 * A103516).
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Dec 01 2007
|
