A143948 Number of permutations of some {1,2,...,k} in which the sum of the positions of the right-to-left minima is n.

1, 1, 1, 3, 7, 28, 130, 759, 5206, 41260, 369043, 3676429, 40334375, 483102302, 6271504796, 87706308280, 1314478069758, 21017345072301, 357096995609668, 6424807487105280, 122024726484398199, 2439707860612958618, 51219795310622022600, 1126569670246506800519

Offset: 0

Author

Emeric Deutsch, Sep 22 2008

Keywords

• nonn

Comments

Column sums of A143947.

Also the number of permutations of some [k] whose cycle maxima sum to n: a(4) = 7: (1)(23), (1234), (1243), (1324), (1342), (1423), (1432). - Alois P. Heinz, Jan 02 2024

Examples

			a(5) = 28 because we have 312, 213, 1342, 1432 and the 24 permutations of {1,2,3,4,5} that end with 1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A143947.

Programs

Maple

g:=sum(product(j+x^(n-j),j=0..n-1),n=0..40): gser:=series(g,x=0,35): seq(coeff(gser,x,n),n=0..23);

Formula

G.f.: Sum_{n>=0} Product_{j=0..n-1} (j+x^(n-j)).

a(n) ~ (n-1)!. - Vaclav Kotesovec, Jun 12 2025

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 09 2023