A171246 Triangle read by rows: T(n,k) = 1 + floor(n!/2^((k - n/2)^2 + 1)).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 7, 13, 7, 1, 1, 13, 51, 51, 13, 1, 1, 23, 181, 361, 181, 23, 1, 1, 34, 530, 2120, 2120, 530, 34, 1, 1, 40, 1261, 10081, 20161, 10081, 1261, 40, 1, 1, 38, 2384, 38144, 152573, 152573, 38144, 2384, 38, 1

Offset

0,5

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 695.

Formula

T(n,k) = 1 + floor(n!/2^((k - n/2)^2 +1)).

Example

Triangle begins as:
   1;
   1,  1;
   1,  2,   1;
   1,  3,   3,    1;
   1,  7,  13,    7,    1;
   1, 13,  51,   51,   13,   1;
   1, 23, 181,  361,  181,  23,  1;
   1, 34, 530, 2120, 2120, 530, 34, 1;

Mathematica

T[n_, k_]:= 1 +Floor[n!*2^(-(k-n/2)^2 -1)]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(PARI) {T(n, k) = 1 + floor(n!/2^((k - n/2)^2 +1))}; \\ G. C. Greubel, Apr 11 2019
(Magma) [[1 +Floor(Factorial(n)/2^((k - n/2)^2 +1)): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 11 2019
(Sage) [[1 + floor(factorial(n)/2^((k-n/2)^2 +1)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 11 2019

Crossrefs

Cf. A171229.

Sequence in context: A225910 A215292 A124975 * A129439 A176469 A141542

Adjacent sequences: A171243 A171244 A171245 * A171247 A171248 A171249

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 06 2009

Extensions

Edited by G. C. Greubel, Apr 11 2019

Status

approved