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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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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);
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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