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A258492
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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.
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2
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42, 1485, 34034, 647920, 11187462, 182587701, 2880017910, 44477796451, 677940669900, 10250875770135, 154278143783022, 2316262521915440, 34742240691197182, 521131993897607925, 7822497290908844702, 117554364707534272375, 1769075045150700563052
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OFFSET
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5,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 5..800
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FORMULA
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a(n) ~ 16^n / (54*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, 5):
seq(a(n), n=5..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, 5];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)
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CROSSREFS
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Column k=5 of A256117.
Sequence in context: A121974 A096048 A215301 * A067638 A155021 A270410
Adjacent sequences: A258489 A258490 A258491 * A258493 A258494 A258495
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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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