cp's OEIS Frontend

A135852 A007318 * A103516 as a lower triangular matrix.

%I A135852 #26 Feb 16 2022 11:03:33
%S A135852 1,3,2,8,4,3,20,6,9,4,48,8,18,16,5,112,10,30,40,25,6,256,12,45,80,75,
%T A135852 36,7,576,14,63,140,175,126,49,8,1280,16,84,224,350,336,196,64,9,2816,
%U A135852 18,108,336,630,756,588,288,81,10
%N A135852 A007318 * A103516 as a lower triangular matrix.
%C A135852 Binomial transform of triangle A103516.
%H A135852 G. C. Greubel, <a href="/A135852/b135852.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A135852 T(n, k) = (A007318 * A103516)(n, k).
%F A135852 T(n, 0) = A001792(n).
%F A135852 Sum_{k=0..n} T(n, k) = A099035(n+1).
%F A135852 T(n, k) = (k+1)*binomial(n, k), with T(n, 0) = (n+2)*2^(n-1), T(n, n) = n+1. - _G. C. Greubel_, Dec 07 2016
%e A135852 First few rows of the triangle are:
%e A135852     1;
%e A135852     3,  2;
%e A135852     8,  4,  3;
%e A135852    20,  6,  9,  4;
%e A135852    48,  8, 18, 16,  5;
%e A135852   112, 10, 30, 40, 25,  6;
%e A135852   256, 12, 45, 80, 75, 36,  7;
%e A135852   ...
%t A135852 T[n_, k_]:= If[n==0, 1, If[k==0, (n+2)*2^(n-1), (k+1)*Binomial[n, k]]];
%t A135852 Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Dec 07 2016 *)
%o A135852 (Sage)
%o A135852 def A135852(n,k):
%o A135852     if (n==0): return 1
%o A135852     elif (k==0): return (n+2)*2^(n-1)
%o A135852     else: return (k+1)*binomial(n, k)
%o A135852 flatten([[A135852(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Feb 07 2022
%Y A135852 Cf. A007318, A103516.
%Y A135852 Cf. A001792 (1st column), A099035 (row sums).
%Y A135852 Cf. A135853 (= A103516 * A007318).
%K A135852 nonn,tabl
%O A135852 0,2
%A A135852 _Gary W. Adamson_, Dec 01 2007
%E A135852 Offset changed to 0 by _G. C. Greubel_, Feb 07 2022