A225960 Number of permutations of [n] having exactly one strong fixed block.

0, 1, 1, 3, 9, 38, 198, 1229, 8819, 71825, 654985, 6615932, 73357572, 886078937, 11583028581, 162939646239, 2454350815033, 39415438078466, 672282146765650, 12137067564016917, 231223273420524311, 4635720862911035149, 97565878042828417209, 2150797149322137710488

Offset

0,4

Comments

See A186373 for the definition of strong fixed blocks.

Links

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..450 (first 201 and last 2 terms from Alois P. Heinz)

Formula

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

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

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

Maple

b:= proc(n) b(n):= -`if`(n<0, 1, add(b(n-i-1)*i!, i=0..n)) end:
a:= n-> add(b(i)*add(b(j), j=0..n-i-1), i=0..n-1):
seq(a(n), n=0..25);

Mathematica

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 *)

Crossrefs

Column k=1 of A186373.

Cf. A052186, A260957.

Sequence in context: A030869 A030846 A030818 * A020121 A270593 A059804

Adjacent sequences: A225957 A225958 A225959 * A225961 A225962 A225963

Keyword

nonn

Author

Alois P. Heinz, May 22 2013

Status

approved