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A262529 Number of partitions of 2n into parts of exactly n sorts which are introduced in ascending order such that sorts of adjacent parts are different. 2
1, 1, 4, 31, 464, 10423, 307123, 11087757, 471750268, 23064505722, 1272685923725, 78185947269685, 5290601944971906, 390900941750607195, 31309282176759170370, 2701913799542547998709, 249913023732255442857064, 24663493072687443375499678 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

a(n) = A262495(2n,n).

a(n) ~ 2^(2*n-2) * (n-1)! / (Pi * sqrt(1-c) * c^(n-1) * (2-c)^n), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599076769581241... - Vaclav Kotesovec, Oct 25 2018

EXAMPLE

a(2) = 4: 3a1b, 2a2b, 2a1b1a, 1a1b1a1b.

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),

      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))

    end:

A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):

a:= n-> add(A(2*n, n-i)*(-1)^i/(i!*(n-i)!), i=0..n):

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

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i == 1, k^(n-1), b[n, i-1, k] + If[i>n, 0, k*b[n-i, i, k]]]; A[n_, k_] := If[n == 0, 1, If[k<2, k, k*b[n, n, k-1]]]; a[n_] := Sum[A[2*n, n-i]*(-1)^i/(i!*(n-i)!), {i, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 07 2017, translated from Maple *)

CROSSREFS

Cf. A262495.

Sequence in context: A319074 A195195 A141827 * A350608 A143077 A203011

Adjacent sequences:  A262526 A262527 A262528 * A262530 A262531 A262532

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 24 2015

STATUS

approved

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Last modified August 8 12:30 EDT 2022. Contains 356009 sequences. (Running on oeis4.)