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 A163774 Row sums of the central coefficients triangle (A163771). 3
 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 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011. Peter Luschny, Swinging Factorial. FORMULA 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). 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: MATHEMATICA sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[(-1)^(n - i)*Binomial[n - k, n - i]*sf[2*i], {i, k, n}]; Table[Sum[t[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 04 2017 *) CROSSREFS Cf. A056040, A163771. Sequence in context: A286182 A101052 A016064 * A304629 A301458 A244784 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 January 27 19:46 EST 2021. Contains 340479 sequences. (Running on oeis4.)