A303617 Decimal expansion of Sum_{k >= 0} 2^(2*k+1)/Product_{i = 0..k} (2*i+1).

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

Offset

1,1

Links

Table of n, a(n) for n=1..93.

Formula

Equals e^2*sqrt(Pi/2)*erf(sqrt(2)) = A072334*A069998*A110894.

Example

8.83943924091904909456698024436203574171002846378309279604186339401138107...
2/1 + 2^3/(1*3) + 2^5/(1*3*5) + 2^7/(1*3*5*7) + 2^9/(1*3*5*7*9) + 2^11/(1*3*5*7*9*11) + 2^13/(1*3*5*7*9*11*13) + ...

Mathematica

RealDigits[E^2 Sqrt[Pi/2] Erf[Sqrt[2]], 10, 100][[1]]

Prog

(PARI) suminf(k=0, 2^(2*k+1)/prod(i=0, k, (2*i+1))) \\ Michel Marcus, Apr 27 2018

Crossrefs

Cf. A001147, A004171.

Cf. A069998, A072334, A110894.

Sequence in context: A219300 A200686 A222066 * A296428 A073447 A011213

Adjacent sequences: A303614 A303615 A303616 * A303618 A303619 A303620

Keyword

nonn,cons

Author

Bruno Berselli, Apr 27 2018

Status

approved