login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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