A014510 a(n) = floor( Gamma(n+1/2) ).

1, 0, 1, 3, 11, 52, 287, 1871, 14034, 119292, 1133278, 11899423, 136843365, 1710542068, 23092317922, 334838609873, 5189998453040, 85634974475162, 1498612053315336, 27724322986333718, 540624298233507504

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..450
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Crossrefs

Cf. A014511, A014512, A014513, A014514, A014516, A014517, A014518, A014521, A014522.

Programs

Maple

seq(floor(evalf(GAMMA(n+1/2),100)), n=0..24);

Mathematica

a[n_] := Floor[Gamma[n + 1/2]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

Formula

a(n)=floor((2n-1)!!/2^n*sqrt(Pi)) where (2n-1)!!=prod(k=1, n, 2*k-1); asymptotically a(n)=n!/sqrt(n)*(1-1/(8n)+1/(128n^2)-5/(1024n^3)+O(1/n^4)) - Benoit Cloitre, Apr 29 2003