A159009 Numerator of the integral of x^n times the Cantor function, from 0 to 1.

1, 5, 11, 233, 97, 36377, 10637, 8885119, 18040327, 107868664309, 19821442673, 2657527033463249, 412093696402361, 28353905269136197727, 57058882710461852501, 30872757660805358101602571

Offset: 0

Author

Simon Tatham (anakin(AT)pobox.com), Apr 02 2009

Keywords

• frac
• nonn

Examples

			I(0) is obviously 1/2 by symmetry.
		

Crossrefs

A095844/A095845 give the integrals of powers of the Cantor function itself.

A159010 gives the corresponding denominators. [From Simon Tatham (anakin(AT)pobox.com), Apr 02 2009]

Programs

Maple

for n from 0 to 20 do CI[n] := 1/(2*(n+1)) + 1/(2*(3^(n+1)-1)) * add(binomial(n,i)*2^(n-i)*CI[i],i=0..n-1); end do;

Formula

I(n) = 1/(2*(n+1)) + 1/(2*3^(n+1)-1) * sum_{i=0}{n-1} (n choose i) 2^(n-i) I(i)