A137988 Decimal expansion of the number whose Pierce expansion has the sequence of double factorial numbers (A000165) as coefficients.

3, 5, 2, 8, 0, 6, 4, 3, 8, 1, 0, 6, 6, 5, 0, 0, 3, 6, 4, 6, 2, 1, 2, 3, 6, 0, 5, 3, 1, 0, 7, 3, 0, 0, 8, 6, 3, 1, 1, 1, 4, 5, 9, 6, 9, 4, 4, 4, 9, 9, 0, 1, 7, 4, 0, 2, 7, 4, 9, 4, 6, 3, 1, 0, 7, 1, 8, 6, 4, 7, 0, 1, 5, 3, 3, 6, 5, 6, 5, 4, 4, 1, 4, 5, 6, 9, 0, 9, 1, 8, 9, 6, 0, 9, 4, 8, 3, 3, 9

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Feb 26 2008

Keywords

• easy
• nonn
• cons

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Eric W. Weisstein, Pierce Expansion.
• Eric W. Weisstein, Engel Expansion.

Crossrefs

Cf. A000142, A137986, A137987, A137989.

Programs

Maple

P:=proc(n) local a,i,j,k,w; a:=0; w:=1; for i from 0 by 1 to n do k:=i; j:=i-2; while j>0 do k:=k*j; j:=j-2; od; if (i=0 or i=1) then k:=1; fi; if i=2 then k:=2; fi; w:=w*k; a:=a+(-1)^i/w; print(evalf(a,100)); od; end: P(100);

Mathematica

RealDigits[N[(Sum[(-1)^n*Product[1/((k + 1)!!), {k, 1, n}], {n, 1, 250}]), 100]][[1]] (* G. C. Greubel, Jan 01 2017 *)