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

Author

Antti Karttunen, Feb 08 2014

Keywords

• nonn
• tabl

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

Crossrefs

Left edge: A003422.

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

Programs

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

Scheme

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

Formula

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