A098697 Euler-Seidel matrix T(k,n) with start sequence A000248, read by antidiagonals.
1, 2, 1, 6, 4, 3, 23, 17, 13, 10, 104, 81, 64, 51, 41, 537, 433, 352, 288, 237, 196, 3100, 2563, 2130, 1778, 1490, 1253, 1057, 19693, 16593, 14030, 11900, 10122, 8632, 7379, 6322, 136064, 116371, 99778, 85748, 73848, 63726, 55094, 47715, 41393
Offset: 0
Examples
1,1,3,10,41,196,1057, 2,4,13,51,237,1253,7379, 6,17,64,288,1490,8632,55094, 23,81,352,1778,10122,63726,437810, 104,433,2130,11900,73848,501536,3687056,
Links
- D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78.
Programs
-
Mathematica
a248[0] = 1; a248[n_] := Sum[Binomial[n, k]*(n - k)^k, {k, 0, n}]; T[0, n_] := T[0, n] = a248[n]; T[k_, n_] := T[k, n] = T[k - 1, n] + T[k - 1, n + 1]; Table[T[k - n, n], {k, 0, 9}, {n, 0, k}] // Flatten (* Jean-François Alcover, Nov 08 2017 *)
Formula
Recurrence: T(0, n) = A000248(n), T(k, n) = T(k-1, n) + T(k-1, n+1).
Comments