A327559 Twice the median of {Stirling2(n, k), k = 0..n}.

1, 2, 2, 2, 11, 30, 84, 254, 717, 1500, 13035, 44550, 300950, 1505504, 3854579, 14283372, 83480149, 251709276, 3136016690, 12605049160, 162391467080, 691231886400, 3678703702014, 23362113269002, 94834621131920, 374452713892530, 4019520663745860, 15252585773825400

Offset

1,2

Comments

"Twice" is included in the definition to handle half-integer medians.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..700

Vaclav Kotesovec, Plot of a(n)/a(n-1) for n = 2..1000

Example

For n = 6, {Stirling2(6, k), k = 0..6} = {0, 1, 31, 90, 65, 15, 1}, so we have 3 elements {0, 1, 1} that are < 15, and 3 elements {31, 90, 65} that are > 15. Hence, 15 is the median, and a(6) = 2*15 = 30.

Maple

a:= n->(l->l[floor(1+n/2)]+l[ceil(1+n/2)])(sort([seq(Stirling2(n, j), j=0..n)])):
seq(a(n), n=1..30);  # Alois P. Heinz, Sep 16 2019

Mathematica

Table[2 Median[Table[StirlingS2[n, k], {k, 0, n}]], {n, 1, 30}]

Prog

(PARI) a(n)={my(t=vecsort(vector(n+1, k, stirling(n, k-1, 2)))); t[n\2+1] + t[n-n\2+1]} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Sequence in context: A068971 A019233 A121223 * A139518 A335986 A152662

Adjacent sequences: A327556 A327557 A327558 * A327560 A327561 A327562

Keyword

nonn,easy

Author

Vladimir Reshetnikov, Sep 16 2019

Status

approved