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%I #15 Jun 01 2022 09:07:13
%S 1,4,26,249,3274,56135,1207433,31638625,987249425,36030130677,
%T 1515621707692,72603595393584,3920675798922189,236615520916677436,
%U 15840357595697061964,1168697367186883073296,94486667847573203169757,8328527812527985862657297,796762955545266206229493979
%N Row 1 of array in A322765.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.
%H Seiichi Manyama, <a href="/A322766/b322766.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = A346500(n,n+1) = A346500(n+1,n). - _Alois P. Heinz_, Jul 21 2021
%p b:= proc(n) option remember; `if`(n=0, 1,
%p add(b(n-j)*binomial(n-1, j-1), j=1..n))
%p end:
%p A:= proc(n, k) option remember; `if`(n<k, A(k, n),
%p `if`(k=0, b(n), (A(n+1, k-1)+add(A(n-k+j, j)
%p *binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))
%p end:
%p a:= n-> A(n, n+1):
%p seq(a(n), n=0..22); # _Alois P. Heinz_, Jul 21 2021
%t b[n_] := b[n] = If[n == 0, 1,
%t Sum[b[n - j]*Binomial[n-1, j-1], {j, 1, n}]];
%t A[n_, k_] := A[n, k] = If[n < k, A[k, n],
%t If[k == 0, b[n], (A[n+1, k - 1] + Sum[A[n - k + j, j]*
%t Binomial[k-1, j], {j, 0, k - 1}] + A[n, k - 1])/2]];
%t a[n_] := A[n, n + 1]; Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Jun 01 2022, after _Alois P. Heinz_ *)
%Y Cf. A322765, A346500.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Dec 30 2018
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