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A227550 A triangle formed like Pascal's triangle, but with factorial(n) on the borders instead of 1. 4

%I

%S 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,

%T 52,154,720,5040,874,206,88,88,206,874,5040,40320,5914,1080,294,176,

%U 294,1080,5914,40320,362880,46234,6994,1374,470,470,1374,6994,46234,362880,3628800

%N A triangle formed like Pascal's triangle, but with factorial(n) on the borders instead of 1.

%C A003422 gives the second column (after 0).

%H Vincenzo Librandi, <a href="/A227550/b227550.txt">Rows n = 0..70, flattened</a>

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 2, 2;

%e 6, 4, 4, 6;

%e 24, 10, 8, 10, 24;

%e 120, 34, 18, 18, 34, 120;

%e 720, 154, 52, 36, 52, 154,720;

%e 5040, 874, 206, 88, 88, 206,874, 5040;

%e 40320, 5914, 1080,294, 176,294,1080,5914,40320;

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

%t 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]

%o (Haskell)

%o a227550 n k = a227550_tabl !! n !! k

%o a227550_row n = a227550_tabl !! n

%o a227550_tabl = map fst $ iterate

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

%o ([1], a001563_list)

%o -- _Reinhard Zumkeller_, Aug 05 2013

%Y 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).

%Y Cf. A003422.

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

%K nonn,tabl

%O 0,4

%A _Vincenzo Librandi_, Aug 04 2013

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)