A237450 Triangle read by rows, T(n,k) = !n + (k-1)*(n-1)!, with n>=1, 1<=k<=n; Position of the first n-letter permutation beginning with number k in the list of lexicographically sorted permutations A030299.

1, 2, 3, 4, 6, 8, 10, 16, 22, 28, 34, 58, 82, 106, 130, 154, 274, 394, 514, 634, 754, 874, 1594, 2314, 3034, 3754, 4474, 5194, 5914, 10954, 15994, 21034, 26074, 31114, 36154, 41194, 46234, 86554, 126874, 167194, 207514, 247834, 288154, 328474, 368794, 409114, 771994, 1134874, 1497754, 1860634, 2223514, 2586394, 2949274, 3312154, 3675034

Offset

1,2

Comments

When organized as a triangular table

1;

2, 3;

4, 6, 8;

10, 16, 22, 28;

34, 58, 82, 106, 130;

...

the k-th term of row n gives the position of the first n-letter permutation beginning with number k among all the lexicographically ordered permutations A030299. Thus the terms give the positions of rows of irregular table A237265 among the rows of A030298.

Note: the notation !n stands for the left factorial, A003422(n).

Links

Antti Karttunen, Rows 1..45 of the triangular table, flattened

Formula

a(n) = A003422(A002024(n)) + (A002262(n-1)*A000142(A002024(n)-1)).

Mathematica

lf[n_] := lf[n] = (-1)^n n! Subfactorial[-n - 1] - Subfactorial[-1] // FullSimplify;
T[n_, k_] := lf[n] + (k - 1)(n - 1)!;
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten

Prog

(Scheme) (define (A237450 n) (+ (A003422 (A002024 n)) (* (A002262 (- n 1)) (A000142 (- (A002024 n) 1)))))

Crossrefs

Left edge: A003422.

Cf. also A002024, A002262, A000142, A030298, A030299, A051683, A237265.

Sequence in context: A211856 A066816 A247334 * A165514 A182417 A189704

Adjacent sequences: A237447 A237448 A237449 * A237451 A237452 A237453

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 08 2014

Status

approved