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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..900 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 Adjacent sequences: A258488 A258489 A258490 * A258492 A258493 A258494 KEYWORD nonn AUTHOR Alois P. Heinz, May 31 2015 STATUS approved

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Last modified March 22 15:35 EDT 2023. Contains 361432 sequences. (Running on oeis4.)