A242938 Decimal expansion of c_e, coefficient associated with the asymptotic evaluation c_e*2^(n^2/4) of the number of subspaces of the n-dimensional vector space over the finite field F_2, n being even.

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.7 Lengyel's constant, p. 318.

Links

G. C. Greubel, Table of n, a(n) for n = 1..2500

Formula

(Sum_(k=-infinity..infinity) q^(-k^2)) / (prod_(j>0) (1-q^(-j))), with q = 2.

Example

7.3719688014613165091531912...

Mathematica

digits = 100; EllipticTheta[3, 0, 1/2]/NProduct[1-2^(-j), {j, 1, Infinity}, WorkingPrecision -> digits + 10, NProductFactors -> digits] // RealDigits[#, 10, digits]& // First
RealDigits[EllipticTheta[3, 0, 1/2]/QPochhammer[1/2, 1/2], 10, 100][[1]] (* Vladimir Reshetnikov, Oct 17 2016 *)

Prog

(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)
th3(1/2)/prodinf(n=1, 1-2.^-n) \\ Charles R Greathouse IV, Jun 06 2016

Crossrefs

Cf. A048651, A086053, A242939, A182176.

Sequence in context: A259453 A096715 A242939 * A085835 A153624 A160578

Adjacent sequences: A242935 A242936 A242937 * A242939 A242940 A242941

Keyword

nonn,cons

Author

Jean-François Alcover, May 27 2014

Status

approved