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

0,2

Comments

In an Euler-Seidel matrix, the rows are consecutive pairwise sums and the columns consecutive differences, with the first column the inverse binomial transform of the start sequence.

Links

Table of n, a(n) for n=0..44.

D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78.

Formula

Recurrence: T(0, n) = A000248(n), T(k, n) = T(k-1, n) + T(k-1, n+1).

Example

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,

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 *)

Crossrefs

First column is A080108, main diagonal is in A098698.

Sequence in context: A329431 A328923 A263271 * A193094 A021466 A286259

Adjacent sequences: A098694 A098695 A098696 * A098698 A098699 A098700

Keyword

nonn,tabl

Author

Ralf Stephan, Sep 23 2004

Status

approved