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 A293202 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} Sum_{j=0..k} j!*x^(j*i). 7
 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 2, 0, 1, 1, 3, 2, 2, 0, 1, 1, 3, 8, 6, 3, 0, 1, 1, 3, 8, 6, 7, 4, 0, 1, 1, 3, 8, 30, 13, 12, 5, 0, 1, 1, 3, 8, 30, 13, 24, 13, 6, 0, 1, 1, 3, 8, 30, 133, 48, 37, 22, 8, 0, 1, 1, 3, 8, 30, 133, 48, 61, 46, 26, 10, 0, 1, 1, 3, 8, 30, 133, 768, 181, 142, 98, 42, 12, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS Seiichi Manyama, Antidiagonals n = 0..139, flattened EXAMPLE Square array begins: 1, 1, 1, 1, 1, ... 0, 1, 1, 1, 1, ... 0, 1, 3, 3, 3, ... 0, 2, 2, 8, 8, ... 0, 2, 6, 6, 30, ... 0, 3, 7, 13, 13, ... MAPLE b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(b(n-i*j, i-1, k)*j!, j=0..min(k, n/i)))) end: A:= (n, k)-> b(n\$2, k): seq(seq(A(n, d-n), n=0..d), d=0..12); # Alois P. Heinz, Oct 02 2017 MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i j, i - 1, k] j!, {j, 0, Min[k, n/i]}]]]; A [n_, k_] := b[n, n, k]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Dec 06 2019, after Alois P. Heinz *) CROSSREFS Columns k=0..5 give A000007, A000009, A293204, A289485, A289486, A293250. Rows n=0..1 give A000012, A057427. Main diagonal gives A161779. Sequence in context: A303913 A117406 A290216 * A280265 A292795 A295028 Adjacent sequences: A293199 A293200 A293201 * A293203 A293204 A293205 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Oct 02 2017 STATUS approved

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Last modified June 12 23:46 EDT 2024. Contains 373362 sequences. (Running on oeis4.)