A225621
Central terms of the triangle in A074911.
Original entry on oeis.org
1, 4, 20, 108, 632, 4060, 28968, 231000, 2058096, 20375964, 222393800, 2653879624, 34365597840, 479776469848, 7181892528272, 114731622081840, 1948073992109280, 35031456100431900, 665075537735997960, 13292908401187179240, 279000321119414475600
Offset: 1
A227550
A triangle formed like Pascal's triangle, but with factorial(n) on the borders instead of 1.
Original entry on oeis.org
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
Offset: 0
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;
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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
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function T(n,k)
if k eq 0 or k eq n then return Factorial(n);
else return T(n-1,k-1) + T(n-1,k);
end if; return T;
end function;
[T(n,k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 02 2021
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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]
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def T(n,k): return factorial(n) if (k==0 or k==n) else T(n-1, k-1) + T(n-1, k)
flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 02 2021
A227791
Central terms of the triangle in A227550.
Original entry on oeis.org
1, 2, 8, 36, 176, 940, 5568, 37128, 280992, 2410812, 23250080, 249164344, 2934303264, 37617633976, 521009920256, 7748175156240, 123095897716800, 2080205257723740, 37253560076385120, 704703668205036120, 14039778681732928800, 293831851498842784680
Offset: 0
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a227791 n = a227550 (2 * n) n
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b:= proc(x, y) option remember; `if`(x=0, y!,
b(x-1, y)+b(sort([x, y-1])[]))
end:
a:= n-> b(n$2):
seq(a(n), n=0..26); # Alois P. Heinz, Jul 14 2021
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T[n_, 0] := n!; T[n_, n_] := n!;
T[n_, k_] /; 0Jean-François Alcover, Nov 03 2022 *)
Showing 1-3 of 3 results.
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