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A322772 Row 2 of array in A322770. 3
2, 9, 70, 801, 12347, 243235, 5908978, 172449180, 5925731200, 235946129714, 10745098631229, 553630279110396, 31978001903989065, 2054387367168242251, 145795148420558536232, 11361381129471379493270, 967044630942570464100761, 89483154423059719127570924, 8963545185499520505954151682 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

a(n) = A346517(n,n+2) = A346517(n+2,n). - Alois P. Heinz, Jul 21 2021

MAPLE

b:= proc(n) option remember; `if`(n=0, 1,

add(b(n-j)*binomial(n-1, j-1), j=1..n))

end:

A:= proc(n, k) option remember; `if`(n<k, A(k, n),

`if`(k=0, b(n), (A(n+1, k-1)-add(A(n-k+j, j)

*binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))

end:

a:= n-> A(n, n+2):

seq(a(n), n=0..18); # Alois P. Heinz, Jul 21 2021

MATHEMATICA

Q[m_, n_] := Q[m, n] = If[n == 0, BellB[m], (1/2)(Q[m+2, n-1] + Q[m+1, n-1] - Sum[Binomial[n-1, k] Q[m, k], {k, 0, n-1}])];

a[n_] := Q[2, n];

Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Apr 29 2022 *)

CROSSREFS

Cf. A322770, A346517.

Sequence in context: A014500 A101482 A099717 * A177450 A193469 A336606

Adjacent sequences: A322769 A322770 A322771 * A322773 A322774 A322775

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 30 2018

STATUS

approved

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Last modified February 4 02:26 EST 2023. Contains 360045 sequences. (Running on oeis4.)