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A185324
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E.g.f. log(1/(2-tan(x)-sec(x))).
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1
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0, 1, 2, 7, 34, 215, 1682, 15727, 171274, 2130275, 29799722, 463123747, 7916886514, 147635940335, 2982555226562, 64888568231767, 1512552803481754, 37608099684426395, 993530210286226202, 27791008680163167787, 820556749933610580994, 25502885614554196884455
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} (k-1)! * A147315(n,k).
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MAPLE
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T:= proc(n, k) option remember;
if k=n then 1
elif k<0 or k>n then 0
else T(n-1, k-1) +k*T(n-1, k) +k*(k+1)/2 *T(n-1, k+1)
fi
end:
a:= n-> add((k-1)! * T(n, k), k=1..n):
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MATHEMATICA
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T[n_, k_] := T[n, k] = If[k==n, 1, If[k<0 || k>n, 0, T[n-1, k-1] + k*T[n-1, k] + k*(k+1)/2*T[n-1, k+1]]]; a[n_] := Sum[(k-1)!*T[n, k], {k, 1, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 03 2015, after Alois P. Heinz *)
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PROG
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(Maxima) a[0]:0$a[1]:1$
a[n]:=sum((-1)^floor(p/2)*(mod(p+1, 2)-(-1)^p*4^floor(p/2))*binomial(n-1, p)*a[n-p], p, 1, n-1)-mod(n-1, 2)*(%i)^n;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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