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 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. 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified June 25 10:09 EDT 2021. Contains 345453 sequences. (Running on oeis4.)