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

%I A143948 #15 Jun 12 2025 02:11:25
%S A143948 1,1,1,3,7,28,130,759,5206,41260,369043,3676429,40334375,483102302,
%T A143948 6271504796,87706308280,1314478069758,21017345072301,357096995609668,
%U A143948 6424807487105280,122024726484398199,2439707860612958618,51219795310622022600,1126569670246506800519
%N A143948 Number of permutations of some {1,2,...,k} in which the sum of the positions of the right-to-left minima is n.
%C A143948 Column sums of A143947.
%C A143948 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
%H A143948 Alois P. Heinz, <a href="/A143948/b143948.txt">Table of n, a(n) for n = 0..200</a>
%F A143948 G.f.: Sum_{n>=0} Product_{j=0..n-1} (j+x^(n-j)).
%F A143948 a(n) ~ (n-1)!. - _Vaclav Kotesovec_, Jun 12 2025
%e A143948 a(5) = 28 because we have 312, 213, 1342, 1432 and the 24 permutations of {1,2,3,4,5} that end with 1.
%p A143948 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);
%Y A143948 Cf. A143947.
%K A143948 nonn
%O A143948 0,4
%A A143948 _Emeric Deutsch_, Sep 22 2008
%E A143948 a(0)=1 prepended by _Alois P. Heinz_, Jul 09 2023