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A322771
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Row 1 of array in A322770.
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3
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1, 3, 18, 172, 2295, 40043, 875936, 23308546, 737478487, 27252363585, 1159335917625, 56103737161197, 3057787510932485, 186102920689311261, 12555513437042340449, 932964243520888524391, 75926403820972271325522, 6733532223196893844825456, 647846856775383975668238328, 67349524752043243630964385000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..300
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FORMULA
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a(n) = A346517(n,n+1) = A346517(n+1,n). - Alois P. Heinz, Jul 21 2021
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MAPLE
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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..19); # Alois P. Heinz, Jul 21 2021
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MATHEMATICA
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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[1, n];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Apr 29 2022 *)
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CROSSREFS
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Cf. A322770, A346517.
Sequence in context: A113130 A289683 A193098 * A177447 A328031 A005192
Adjacent sequences: A322768 A322769 A322770 * A322772 A322773 A322774
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Dec 30 2018
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STATUS
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approved
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