A248696 Decimal expansion of sum_{n >= 1} (2n)!/(1!*2!*...*n!).

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

Offset: 3

Author

Clark Kimberling, Oct 13 2014

Keywords

• nonn
• easy
• cons

Comments

Let t(n) = (2n)!/(1!*2!*...*n!). Then t(n) is an integer for n = 1..5, and max{t(n), n >= 1} = t(4) = 140... . It appears that t(n) < 10^(-6) for n > 9.

Examples

			338.9492801098942429745072350488697681125523042506474491612493021261451367444...
		

Crossrefs

Cf. A214869, A248695.

Programs

Maple

evalf(sum((2*n)!/product(k!, k=1..n), n=1..infinity), 120); # Vaclav Kotesovec, Oct 19 2014

Mathematica

u = N[Sum[(2 n)!/Product[k!, {k, 1, n}], {n, 1, 300}], 120]
RealDigits[u]  (* A248696 *)
NSum[(2 n)!/BarnesG[n+2], {n, 1, Infinity}, WorkingPrecision -> 103] // RealDigits // First (* Jean-François Alcover, Nov 19 2015 *)

PARI

suminf(n=1, (2*n)!/prod(k=1, n, k!)) \\ Michel Marcus, Oct 19 2014

Extensions

More digits from Jean-François Alcover, Nov 19 2015