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A258491
Number of words of length 2n such that all letters of the quaternary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting doublets into the initially empty word.
2
14, 300, 4400, 55692, 657370, 7488228, 83752760, 928406556, 10254052556, 113186465340, 1250820198264, 13852280754980, 153813849202674, 1712835575525140, 19129590267619304, 214261857777632700, 2406509409480345364, 27100348605141932540, 305944173898725745944
OFFSET
4,1
LINKS
FORMULA
a(n) ~ 12^n / (8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
end:
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 4):
seq(a(n), n=4..25);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n == 0, 1, (k/n) Sum[Binomial[2n, j] (n - j)* If[j == 0, 1, (k - 1)^j], {j, 0, n - 1}]];
T[n_, k_] := Sum[(-1)^i A[n, k - i]/(i! (k - i)!), {i, 0, k}];
a[n_] := T[n, 4];
a /@ Range[4, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A256117.
Sequence in context: A186376 A034834 A276699 * A251220 A205619 A034912
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 31 2015
STATUS
approved