A362113 Truncate Stirling's asymptotic series for 1! after n terms and round to the nearest integer.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 12, 13, -131, -144, 1878, 2047, -31243, -34023, 603493, 656720, -13392786, -14565501, 338472513, 367934625, -9665776360, -10502979551, 309738982467, 336455915833, -11068897604205, -12020303454921, 438669580592210
Offset: 0
Keywords
Links
- 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)
Programs
-
Maple
h := proc(k) option remember; local j; `if`(k=0, 1, (h(k-1)/k-add((h(k-j)*h(j))/(j+1), j=1..k-1))/(1+1/(k+1))) end: StirlingAsympt := proc(n) option remember; h(2*n)*2^n*pochhammer(1/2, n) end: c := n -> StirlingAsympt(n); # # Peter Luschny, Feb 08 2011 (This is A001163(n)/A001164(n)). S:=proc(k,N) local i; global c; sqrt(2*Pi)*N^(N+1/2)*exp(-N)*add(c(i)/N^i,i=0..k); end; Digits:=200; T:=proc(N,M) local k; [seq(round(evalf(S(k,N))),k=0..M)]; end; T(1,40);
Comments