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 A163775 Row sums of triangle A163772. 2
 1, 11, 73, 403, 2021, 9567, 43611, 193683, 844213, 3629083, 15437951, 65143503, 273148279, 1139548469, 4734740493, 19606960755, 80969809797, 333601494651 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Peter Luschny, Swinging Factorial. FORMULA a(n) = Sum_{k=0..n} Sum_{i=k..n} (-1)^(n-i)*binomial(n-k,n-i)*(2i+1)\$ where i\$ denotes the swinging factorial of i (A056040). MAPLE swing := proc(n) option remember; if n = 0 then 1 elif irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end: a := proc(n) local i, k; add(add((-1)^(n-i)*binomial(n-k, n-i)*swing(2*i+1), i=k..n), k=0..n) end: MATHEMATICA sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[(-1)^(n - i)* Binomial[n - k, n - i]*sf[2*i + 1], {i, k, n}]; Table[Sum[t[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 04 2017 *) CROSSREFS Cf. A163772. Sequence in context: A123039 A226034 A217946 * A092244 A155634 A003367 Adjacent sequences:  A163772 A163773 A163774 * A163776 A163777 A163778 KEYWORD nonn AUTHOR Peter Luschny, Aug 05 2009 STATUS approved

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