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A258492
Number of words of length 2n such that all letters of the quinary 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
42, 1485, 34034, 647920, 11187462, 182587701, 2880017910, 44477796451, 677940669900, 10250875770135, 154278143783022, 2316262521915440, 34742240691197182, 521131993897607925, 7822497290908844702, 117554364707534272375, 1769075045150700563052
OFFSET
5,1
LINKS
FORMULA
a(n) ~ 16^n / (54*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, 5):
seq(a(n), n=5..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, 5];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A256117.
Sequence in context: A121974 A096048 A215301 * A067638 A155021 A270410
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 31 2015
STATUS
approved