OFFSET
0,5
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
N. J. A. Sloane, Transforms
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, ...
2, 7, 14, 23, 34, ...
7, 38, 93, 178, 299, ...
38, 291, 822, 1763, 3270, ...
MAPLE
hymtr:= proc(p) proc(n, m) `if`(m=0, p(n), m*add(p(k) *binomial(n, k) *(n-k+m)^(n-k-1), k=0..n)) end end: f:= proc(n) option remember; add(add(binomial(m, j) *binomial(n-1, n-m-j) *n^(n-m-j) *(m+j)!/ (-2)^j/ m!, j=0..m), m=0..n) end: A:= hymtr(f): seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
hymtr[p_] := Function[{n, m}, If[m == 0, p[n], m*Sum[p[k]*Binomial[n, k]*(n-k+m)^(n-k-1), {k, 0, n}]]]; f[0] = 1; f[n_] := f[n] = Sum[Sum[Binomial[m, j]*Binomial[n-1, n-m-j]*n^(n-m-j)*(m+j)!/(-2)^j/m!, {j, 0, m}], {m, 0, n}]; A[0, _] = 1; A[1, k_] := k+1; A[n_, m_] := hymtr[f][n, m]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Dec 27 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 17 2008
STATUS
approved