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 A296663 Row sums of A296664. 3
 1, 1, 4, 7, 20, 38, 96, 187, 444, 874, 2000, 3958, 8840, 17548, 38528, 76627, 166124, 330818, 710256, 1415650, 3016056, 6015316, 12736064, 25413342, 53530840, 106853668, 224107936, 447472972, 935062544, 1867450648, 3890018816, 7770342787, 16141765964 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..32. FORMULA a(n) = 2^n*(2*h(n)/sqrt(Pi) - 1) where h(n) = (n/2+1)*Gamma((n+1)/2)/Gamma((n+2)/2) if n mod 2 = 0 else Gamma((n+4)/2)/Gamma((n+3)/2). a(n) = 2^n*((n+2+(n mod 2))*binomial((n-1+3*(n mod 2))/2, -1/2) - 1). -(n+1)*(n^2-2*n-1) *a(n) +2*(n-2)*(n^2+n+1) *a(n-1) +4*(n-1)*(n^2-n-5) *a(n-2) -8*(n-2)*(n^2-2) *a(n-3)=0. - R. J. Mathar, Jan 03 2018 MAPLE a := proc(n) if n mod 2 = 0 then ((n+2)/2)*GAMMA((n+1)/2)/GAMMA((n+2)/2) else GAMMA((n+4)/2)/GAMMA((n+3)/2) fi; 2^n*(2*%/sqrt(Pi)-1) end: seq(a(n), n=0..32); MATHEMATICA a[n_] := 2^n ((n + 2 + Mod[n, 2]) Binomial[(n - 1 + 3 Mod[n, 2])/2, -1/2] - 1); Table[a[n], {n, 0, 32}] CROSSREFS Cf. A296664, A000531 (bisection). Sequence in context: A049947 A266822 A296624 * A066345 A355357 A026570 Adjacent sequences: A296660 A296661 A296662 * A296664 A296665 A296666 KEYWORD nonn AUTHOR Peter Luschny, Dec 19 2017 STATUS approved

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Last modified May 24 23:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)