cp's OEIS Frontend

A113143 Table T(n,k), n >= 0 and k >= 0, read by antidiagonals, related to A111146.

%I A113143 #12 Apr 01 2017 21:04:56
%S A113143 1,1,1,1,1,2,1,1,2,4,1,1,2,5,8,1,1,2,6,15,16,1,1,2,7,26,54,32,1,1,2,8,
%T A113143 41,158,235,64,1,1,2,9,60,364,1282,1237,128,1,1,2,10,83,708,4409,
%U A113143 13158,7790,256,1,1,2,11,110,1226,11428,67563,163354
%N A113143 Table T(n,k), n >= 0 and k >= 0, read by antidiagonals, related to A111146.
%C A113143 Let R(m,n,k), 0 <= k <= n, the Riordan array (1, x*g(x)) where g(x)is g.f. of the m-fold factorials.
%C A113143 Then the row sums of R(m,n,k) are given by row m; example: m = 1, R(1,n,k) = A084938(n,k) and A051295 gives the row sums of A084938.
%C A113143 Square array of INVERT of m-fold factorials.
%F A113143 T(n, k) = Sum_{j=0..k} n^(k-j)*A111146(k, j).
%e A113143 Table begins:
%e A113143 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, ...
%e A113143 1, 1, 2, 5, 15, 54, 235, 1237, 7790, 57581, 489231, 4690254, ...
%e A113143 1, 1, 2, 6, 26, 158, 1282, 13158, 163354, 2374078, 39456386, ...
%e A113143 1, 1, 2, 7, 41, 364, 4409, 67573, 1248626, 26948347, 664414997, ...
%e A113143 1, 1, 2, 8, 60, 708, 11428, 232756, 5704964, 163192820, 5331728964, ...
%e A113143 1, 1, 2, 9, 83, 1226, 24727, 627909, 19169758, 682800001, 27776711627, ...
%e A113143 1, 1, 2, 10, 110, 1954, 47270, 1437562, 52531310, 2239259266, 109021857446, ...
%e A113143 1, 1, 2, 11, 141, 2928, 82597, 2925973, 124502114, 6179425823, 350316271761, ...
%e A113143 1, 1, 2, 12, 176, 4184, 134824, 5451528, 264710536, 14992543432, 969925065992, ...
%e A113143 1, 1, 2, 13, 215, 5758, 208643, 9481141, 517310894, 32922122485, 2393313188039, ...
%e A113143 1, 1, 2, 14, 258, 7686, 309322, 15604654, 945111938, 66766075046, 5387893860042, ...
%o A113143 (PARI) {T(n,k)=local(x=X+X*O(X^k),y=Y+Y*O(Y^k));A=1/(1-x*y*sum(j=0,k,x^j*prod(i= 0,j-1,y+i)));return(sum(m=0,k,n^(k-m)*polcoeff(polcoeff(A,k,X),m,Y)))}
%Y A113143 Cf. A051295 (row n=1), A112934 (row n=2), A113144 (row n = 3), A113145 (row n=4), A113146 (row n=5), A113147 (row n = 6), A113148 (row n=7), A113149 (row n=8).
%K A113143 nonn,tabl
%O A113143 0,6
%A A113143 _Philippe Deléham_ and _Paul D. Hanna_, Oct 30 2005