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A322767 Row 2 of array in A322765. 3
2, 11, 92, 1075, 16601, 325269, 7837862, 226700129, 7720099374, 304732680254, 13763771702539, 703691774091622, 40351866669219915, 2574830780826344436, 181574292457398520558, 14065771632972561098569, 1190588796562104776974207 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..300

FORMULA

a(n) = A346500(n,n+2) = A346500(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..22);  # Alois P. Heinz, Jul 21 2021

MATHEMATICA

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

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

Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Apr 29 2022 *)

CROSSREFS

Cf. A322765, A346500.

Sequence in context: A222080 A122708 A337012 * A292424 A225623 A005366

Adjacent sequences:  A322764 A322765 A322766 * A322768 A322769 A322770

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 30 2018

STATUS

approved

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Last modified August 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)