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 A321400 A family of sequences converging to the exponential limit of sec + tan (A320956). Square array A(n, k) for n >= 0 and k >= 0, read by descending antidiagonals. 1
 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 5, 8, 2, 1, 1, 0, 16, 40, 10, 2, 1, 1, 0, 61, 256, 70, 10, 2, 1, 1, 0, 272, 1952, 656, 75, 10, 2, 1, 1, 0, 1385, 17408, 7442, 816, 75, 10, 2, 1, 1, 0, 7936, 177280, 99280, 11407, 832, 75, 10, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS See the comments and definitions in A320956. Note also the corresponding construction for the exp function in A320955. LINKS EXAMPLE Array starts: n\k 0 1 2 3 4 5 6 7 8 ... ------------------------------------------------------- [0] 1, 0, 0, 0, 0, 0, 0, 0, 0, ... A000007 [1] 1, 1, 1, 2, 5, 16, 61, 272, 1385, ... A000111 [2] 1, 1, 2, 8, 40, 256, 1952, 17408, 177280, ... A000828 [3] 1, 1, 2, 10, 70, 656, 7442, 99280, 1515190, ... A320957 [4] 1, 1, 2, 10, 75, 816, 11407, 194480, 3871075, ... A321394 [5] 1, 1, 2, 10, 75, 832, 12322, 232560, 5325325, ... [6] 1, 1, 2, 10, 75, 832, 12383, 238272, 5693735, ... [7] 1, 1, 2, 10, 75, 832, 12383, 238544, 5732515, ... [8] 1, 1, 2, 10, 75, 832, 12383, 238544, 5733900, ... ------------------------------------------------------- Seen as a triangle given by descending antidiagonals: [0] 1 [1] 0, 1 [2] 0, 1, 1 [3] 0, 1, 1, 1 [4] 0, 2, 2, 1, 1 [5] 0, 5, 8, 2, 1, 1 [6] 0, 16, 40, 10, 2, 1, 1 [7] 0, 61, 256, 70, 10, 2, 1, 1 MAPLE sf := proc(n) option remember; `if`(n <= 1, 1-n, (n-1)*(sf(n-1) + sf(n-2))) end: kernel := proc(n, k) option remember; binomial(n, k)*sf(k) end: egf := n -> add(kernel(n, k)*((tan + sec)(x*(n - k))), k=0..n): A321400Row := proc(n, len) series(egf(n), x, len + 2): seq(coeff(%, x, k)*k!/n!, k=0..len) end: seq(lprint(A321400Row(n, 9)), n=0..9); CROSSREFS Cf. A000111 (n=1), A000828 (n=2), A320957 (n=3), A321394 (n=4), A320956 (limit). Antidiagonal sums (and row sums of the triangle): A321399. Sequence in context: A004564 A300705 A144157 * A004562 A261817 A123550 Adjacent sequences: A321397 A321398 A321399 * A321401 A321402 A321403 KEYWORD nonn,tabl AUTHOR Peter Luschny, Nov 08 2018 STATUS approved

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Last modified March 30 20:57 EDT 2023. Contains 361623 sequences. (Running on oeis4.)