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A258491
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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.
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2
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14, 300, 4400, 55692, 657370, 7488228, 83752760, 928406556, 10254052556, 113186465340, 1250820198264, 13852280754980, 153813849202674, 1712835575525140, 19129590267619304, 214261857777632700, 2406509409480345364, 27100348605141932540, 305944173898725745944
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OFFSET
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4,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 4..900
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FORMULA
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a(n) ~ 12^n / (8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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Column k=4 of A256117.
Sequence in context: A186376 A034834 A276699 * A251220 A205619 A034912
Adjacent sequences: A258488 A258489 A258490 * A258492 A258493 A258494
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, May 31 2015
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STATUS
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approved
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