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#40 by Alois P. Heinz at Tue Apr 20 12:58:35 EDT 2021
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#39 by Alois P. Heinz at Tue Apr 20 12:57:52 EDT 2021
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| CROSSREFS
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Cf. Column k=0 of A047921.
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| STATUS
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approved
editing
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#38 by Susanna Cuyler at Sat May 23 14:30:36 EDT 2020
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#37 by Jean-François Alcover at Sat May 23 08:31:38 EDT 2020
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#36 by Jean-François Alcover at Sat May 23 08:31:32 EDT 2020
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| MATHEMATICA
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d[0] = 1; d[n_] := d[n] = n d[n - 1] + (-1)^n;
T[n_, k_] := If[n == 0 && k == 0, 1, If[k <= n/2, Binomial[n - k, k] d[n + 1 - k]/(n - k), 0]];
a[n_] := Sum[T[n, k], {k, 0, Quotient[n, 2]}];
a /@ Range[0, 25] (* Jean-François Alcover, May 23 2020 *)
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| STATUS
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approved
editing
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#35 by Alois P. Heinz at Sun Jul 21 17:43:12 EDT 2019
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#34 by Alois P. Heinz at Sun Jul 21 17:43:07 EDT 2019
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| LINKS
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Alois P. Heinz, <a href="/A002628/b002628.txt">Table of n, a(n) for n = 0..450</a>
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#33 by Alois P. Heinz at Sun Jul 21 17:40:47 EDT 2019
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| MAPLE
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# third Maple program:
a:= proc(n) option remember; `if`(n<5,
[1$2, 2, 5, 21][n+1], (n-3)*a(n-1)+(3*n-6)*a(n-2)+
(4*n-12)*a(n-3)+(3*n-12)*a(n-4)+(n-5)*a(n-5))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Jul 21 2019
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#32 by Alois P. Heinz at Sun Jul 21 17:35:16 EDT 2019
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#31 by Alois P. Heinz at Sun Jul 21 17:25:39 EDT 2019
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| MAPLE
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d[-1]:= 0: for n from 0 to 51 do d[n] := n*d[n-1]+(-1)^n end do: a:= proc(n) add(binomial(n-k, k)*(d[n-k]+d[n-k-1]), k = 0..floor((1/2)*n)) end proc: seq(a(n), n = 0..25); # Emeric Deutsch, Sep 06 2010
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