A225960 - OEIS

%I #23 Oct 06 2015 11:48:35

%S 0,1,1,3,9,38,198,1229,8819,71825,654985,6615932,73357572,886078937,

%T 11583028581,162939646239,2454350815033,39415438078466,

%U 672282146765650,12137067564016917,231223273420524311,4635720862911035149,97565878042828417209,2150797149322137710488

%N Number of permutations of [n] having exactly one strong fixed block.

%C See A186373 for the definition of strong fixed blocks.

%H Alois P. Heinz and Vaclav Kotesovec, <a href="/A225960/b225960.txt">Table of n, a(n) for n = 0..450</a> (first 201 and last 2 terms from Alois P. Heinz)

%F a(n) = Sum_{1<=i<=j<=n} A052186(i-1) * A052186(n-j).

%F a(n) = Sum_{i=0..n-1} A052186(i) * Sum_{j=0..n-i-1} A052186(j).

%F a(n) ~ 2 * (n-1)! * (1 - 1/n + 2/n^3 + 11/n^4 + 97/n^5 + 1105/n^6 + 13905/n^7 + 189633/n^8 + 2803873/n^9 + 44875599/n^10), for coefficients see A260957. - _Vaclav Kotesovec_, Aug 29 2014, extended Aug 05 2015

%p b:= proc(n) b(n):= -`if`(n<0, 1, add(b(n-i-1)*i!, i=0..n)) end:

%p a:= n-> add(b(i)*add(b(j), j=0..n-i-1), i=0..n-1):

%p seq(a(n), n=0..25);

%t nmax = 25; A052186zero = Rest[CoefficientList[Assuming[Element[x, Reals], Series[-1/(ExpIntegralEi[1/x]/E^(1/x) + 1), {x, 0, nmax+1}]], x]]; suma = ConstantArray[0, nmax+1]; s = 0; Do[s = s + A052186zero[[j+1]]; suma[[j+1]] = s, {j, 0, nmax}]; Flatten[{0, Table[Sum[A052186zero[[i+1]]*suma[[n-i]], {i, 0, n-1}], {n, 1, nmax}]}] (* _Vaclav Kotesovec_, Aug 05 2015, more efficient program for big nmax *)

%Y Column k=1 of A186373.

%Y Cf. A052186, A260957.

%K nonn

%O 0,4

%A _Alois P. Heinz_, May 22 2013