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A163774 Row sums of the central coefficients triangle (A163771). 2
1, 3, 13, 51, 201, 783, 3039, 11763, 45481, 175803, 679779, 2630367, 10187659, 39500373, 153329913, 595883763, 2318471289, 9030982491, 35216266947, 137469149451, 537152523711, 2100857828193, 8223917499477, 32219655346719, 126328429601451, 495676719721953, 1946227355491909 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = Sum_{k=0..n} Sum_{i=k..n} (-1)^(n-i)*binomial(n-k,n-i)*(2i)$, where i$ denotes the swinging factorial of i (A056040).

REFERENCES

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

Table of n, a(n) for n=0..26.

Peter Luschny, Swinging Factorial.

FORMULA

Conjecture: a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n+1,k)*binomial(2*k,k). - Werner Schulte, Nov 17 2015

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), i=k..n), k=0..n) end:

CROSSREFS

Cf. A056040, A163771.

Sequence in context: A026529 A101052 A016064 * A244784 A197074 A014985

Adjacent sequences:  A163771 A163772 A163773 * A163775 A163776 A163777

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 05 2009

EXTENSIONS

More terms from Michel Marcus, Nov 24 2015

STATUS

approved

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Last modified March 27 06:50 EDT 2017. Contains 284144 sequences.