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A258499 Number of words of length 4n such that all letters of the n-ary 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. 3
1, 1, 34, 3509, 657370, 182587701, 67773956250, 31600247019120, 17769492060922914, 11710509049983422030, 8855064908059488718600, 7558849413204728468703991, 7190781941414575290014093320, 7544364858457252265315311530675, 8654711454787575656983217747533920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

FORMULA

a(n) = A256117(2n,n).

a(n) ~ c * d^n * n! / n^(5/2), where d = A256254 = 98.82487375173568573170688..., c = 0.008372249434869139279228556376854454452398... . - 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(2*n, n):

seq(a(n), n=0..20);

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[2n, n];

a /@ Range[0, 20] (* Jean-Fran├žois Alcover, Dec 21 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A256117.

Sequence in context: A252709 A138590 A069223 * A218718 A129056 A212034

Adjacent sequences:  A258496 A258497 A258498 * A258500 A258501 A258502

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 31 2015

STATUS

approved

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Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)