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A227550 A triangle formed like Pascal's triangle, but with factorial(n) on the borders instead of 1. 4
1, 1, 1, 2, 2, 2, 6, 4, 4, 6, 24, 10, 8, 10, 24, 120, 34, 18, 18, 34, 120, 720, 154, 52, 36, 52, 154, 720, 5040, 874, 206, 88, 88, 206, 874, 5040, 40320, 5914, 1080, 294, 176, 294, 1080, 5914, 40320, 362880, 46234, 6994, 1374, 470, 470, 1374, 6994, 46234, 362880, 3628800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A003422 gives the second column (after 0).

LINKS

Vincenzo Librandi, Rows n = 0..70, flattened

EXAMPLE

Triangle begins:

1;

1,     1;

2,     2,    2;

6,     4,    4,   6;

24,    10,   8,   10,  24;

120,   34,   18,  18,  34, 120;

720,   154,  52,  36,  52, 154,720;

5040,  874,  206, 88,  88, 206,874, 5040;

40320, 5914, 1080,294, 176,294,1080,5914,40320;

362880,46234,6994,1374,470,470,1374,6994,46234,362880; etc.

MATHEMATICA

t = {}; Do[r = {}; Do[If[k == 0||k == n, m = n!, m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t = Flatten[t]

PROG

(Haskell)

a227550 n k = a227550_tabl !! n !! k

a227550_row n = a227550_tabl !! n

a227550_tabl = map fst $ iterate

   (\(vs, w:ws) -> (zipWith (+) ([w] ++ vs) (vs ++ [w]), ws))

   ([1], a001563_list)

-- Reinhard Zumkeller, Aug 05 2013

CROSSREFS

Cf. similar triangles with t on the borders: A007318 (t = 1), A028326 (t = 2), A051599 (t = prime(n)), A051601 (t = n), A051666 (t = n^2), A108617 (t = fibonacci(n)), A134636 (t = 2n+1), A137688 (t = 2^n), A227075 (t = 3^n).

Cf. A003422.

Cf. A227791 (central terms), A001563, A074911.

Sequence in context: A119918 A084867 A194949 * A286384 A099259 A131904

Adjacent sequences:  A227547 A227548 A227549 * A227551 A227552 A227553

KEYWORD

nonn,tabl

AUTHOR

Vincenzo Librandi, Aug 04 2013

STATUS

approved

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Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)