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1, 5, 24, 111, 500, 2210, 9632, 41531, 177564, 754014, 3184016, 13382710, 56026984, 233765636, 972504704, 4035441491, 16707488684, 69033916166, 284733161264, 1172510645666, 4821324991064, 19799091571676, 81208982686784, 332726301861086, 1361862906980120
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1)).
a(n) = 4^n*((2*(n + 2)*Gamma(n + 3/2))/(sqrt(Pi)*Gamma(n + 2)) - 1).
a(n) = (n/2+1)*binomial(2*(n+1), n+1) - 4^n.
a(n) ~ 4^n*(2*sqrt(n/Pi) - 1).
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MAPLE
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A296770 := n -> add(binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1), k=0..n):
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MATHEMATICA
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a[n_] := 4^n ((2 (2 + n) Gamma[3/2 + n])/(Sqrt[Pi] Gamma[2 + n]) - 1);
Table[a[n], {n, 0, 24}]
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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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