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A322766 Row 1 of array in A322765. 3
1, 4, 26, 249, 3274, 56135, 1207433, 31638625, 987249425, 36030130677, 1515621707692, 72603595393584, 3920675798922189, 236615520916677436, 15840357595697061964, 1168697367186883073296, 94486667847573203169757, 8328527812527985862657297, 796762955545266206229493979 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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+1) = A346500(n+1,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+1):

seq(a(n), n=0..22);  # Alois P. Heinz, Jul 21 2021

MATHEMATICA

b[n_] := b[n] = If[n == 0, 1,

     Sum[b[n - j]*Binomial[n-1, j-1], {j, 1, n}]];

A[n_, k_] := A[n, k] = If[n < k, A[k, n],

     If[k == 0, b[n], (A[n+1, k - 1] + Sum[A[n - k + j, j]*

     Binomial[k-1, j], {j, 0, k - 1}] + A[n, k - 1])/2]];

a[n_] := A[n, n + 1];  Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Jun 01 2022, after Alois P. Heinz *)

CROSSREFS

Cf. A322765, A346500.

Sequence in context: A210918 A052880 A090357 * A160886 A192546 A213438

Adjacent sequences:  A322763 A322764 A322765 * A322767 A322768 A322769

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 30 2018

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)