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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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Last modified August 20 17:05 EDT 2017. Contains 290836 sequences.