0,6

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.

Then the row sums of R(m,n,k) is given by the row m; example : m = 1, R(1,n,k) = A084938(n,k) and A051295 gives the row sums of A084938.

Square array of INVERT of m-fold factorials.

T(n, k) = Sum_{j=0..k} n^(k-j)*A111146(k, j).

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, ...

(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)))}

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).

Sequence in context: A027935 A137940 A137855 this_sequence A136788 A136450 A131054

Adjacent sequences: A113140 A113141 A113142 this_sequence A113144 A113145 A113146

nonn,tabl

Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Oct 30 2005