A258467 Number of partitions of 2n into parts of exactly n sorts which are introduced in ascending order.

1, 2, 12, 130, 2216, 52078, 1558219, 56524414, 2406802476, 117575627562, 6478447651345, 397345158550386, 26842747368209994, 1980156804133210116, 158365138356099680582, 13647670818304698139989, 1260732993182758276252088, 124273946254095006307105363

Offset

0,2

Links

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

Formula

a(n) = A256130(2n,n).

a(n) ~ 2^(2*n-1/2) * n^(n-1/2) / (sqrt(Pi*(1-c)) * exp(n) * c^n * (2-c)^n), where c = -A226775 = -LambertW(-2*exp(-2)) = 0.4063757399599599... . - Vaclav Kotesovec, May 31 2015

a(n) ~ Stirling2(2*n, n) = A007820(n). - Vaclav Kotesovec, Jun 01 2015

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
    end:
T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> T(2*n, n):
seq(a(n), n=0..20);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1, 0, b[n, i-1, k] + If[i>n, 0, k*b[n-i, i, k]]]]; T[n_, k_] := Sum[b[n, n, k-i]*(-1)^i/(i!*(k-i)!), {i, 0, k}]; a[n_] := T[2n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 06 2017, translated from Maple *)

Crossrefs

Cf. A256130, A187655, A187657, A217899, A217900, A245109, A319732.

Sequence in context: A365601 A185751 A090361 * A286422 A073551 A215363

Adjacent sequences: A258464 A258465 A258466 * A258468 A258469 A258470

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved