0,2

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, December 1972, p. 257, Eq. 6.1.37.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 267, #23.

T. Mueller, Finite group actions and asymptotic expansion of e^P(z), Combinatorica, 17 (4) (1997), 523-554.

J. W. Wrench, Jr., Concerning two series for the gamma function, Math. Comp., 22 (1968), 617-626.

G. Marsaglia and J. C. W. Marsaglia, A new derivation of Stirling's approximation to n!, Amer. Math. Monthly, 97 (1990), 827-829. MR1080390 (92b:41049)

T. D. Noe, Table of n, a(n) for n=0..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 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, December 1972, p. 257, Eq. 6.1.37.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

The coefficients c_k have g.f. 1 + Sum_{k >= 1} c_k/z^k = exp( Sum_{k >= 1} B_{2k}/(2k(2k-1)z^(2k-1)) ).

Gamma(z) ~ sqrt(2 Pi) z^(z-1/2) e^(-z) (1 + 1/(12 z) + 1/(288 z^2) - 139/(51840 z^3) - 571/(2488320 z^4) + ... ), z -> infinity in |arg z| < Pi.

Denominator[ Reverse[ Drop[ CoefficientList[ Simplify[ PowerExpand[ Normal[ Series[n!, {n, Infinity, 17}]]Exp[n]/(Sqrt[2Pi n]*n^(n - 17))]], n], 1]]]

(PARI) a(n)=local(A, m); if(n<1, n==0, A=vector(m=2*n+1, k, 1); for(k=2, m, A[k]=(A[k-1]-sum(i=2, k-1, i*A[i]*A[k+1-i]))/(k+1)); denominator(A[m]*m!/2^n/n!)) /* Michael Somos Jun 09 2004 */

Cf. A001163.

Sequence in context: A009604 A079519 A077424 this_sequence A041267 A041264 A109867

Adjacent sequences: A001161 A001162 A001163 this_sequence A001165 A001166 A001167

nonn,frac,nice

njas

More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 14 2001