A113143 Table T(n,k), n >= 0 and k >= 0, read by antidiagonals, related to A111146.
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, 41, 158, 235, 64, 1, 1, 2, 9, 60, 364, 1282, 1237, 128, 1, 1, 2, 10, 83, 708, 4409, 13158, 7790, 256, 1, 1, 2, 11, 110, 1226, 11428, 67563, 163354
Offset: 0
Examples
Table begins: 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, ... 1, 1, 2, 5, 15, 54, 235, 1237, 7790, 57581, 489231, 4690254, ... 1, 1, 2, 6, 26, 158, 1282, 13158, 163354, 2374078, 39456386, ... 1, 1, 2, 7, 41, 364, 4409, 67573, 1248626, 26948347, 664414997, ... 1, 1, 2, 8, 60, 708, 11428, 232756, 5704964, 163192820, 5331728964, ... 1, 1, 2, 9, 83, 1226, 24727, 627909, 19169758, 682800001, 27776711627, ... 1, 1, 2, 10, 110, 1954, 47270, 1437562, 52531310, 2239259266, 109021857446, ... 1, 1, 2, 11, 141, 2928, 82597, 2925973, 124502114, 6179425823, 350316271761, ... 1, 1, 2, 12, 176, 4184, 134824, 5451528, 264710536, 14992543432, 969925065992, ... 1, 1, 2, 13, 215, 5758, 208643, 9481141, 517310894, 32922122485, 2393313188039, ... 1, 1, 2, 14, 258, 7686, 309322, 15604654, 945111938, 66766075046, 5387893860042, ...
Crossrefs
Programs
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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)))}
Formula
T(n, k) = Sum_{j=0..k} n^(k-j)*A111146(k, j).
Comments