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 A098697 Euler-Seidel matrix T(k,n) with start sequence A000248, read by antidiagonals. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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: A162312 A141715 A263271 * A193094 A021466 A286259 Adjacent sequences:  A098694 A098695 A098696 * A098698 A098699 A098700 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Sep 23 2004 STATUS approved

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Last modified June 22 17:19 EDT 2018. Contains 305672 sequences. (Running on oeis4.)