A078801 Expansion of Gaussian product of arithmetic mean and Lehmer mean evaluated at 1 + 4*x.

1, 2, 2, -4, 10, -28, 76, -184, 378, -620, 708, -328, -36, -4008, 25960, -83984, 135066, 188788, -2232236, 9070040, -23335660, 29933128, 69732568, -630906096, 2551027132, -7193660232, 13576199192, -5110303664, -92186317112

Offset

0,2

References

J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 265-266, Exercise 7.

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: A(x) satisfies A(x) = (1 + 2*x) * A(x^2 / (1 + 2*x)^2), A(0) = 1.

a(n) = (-1)^n * Sum_{k>0} 2^(n - 2*k) * a(k) * binomial(n-2, n-2*k), n>1.

Example

1 + 2*x + 2*x^2 - 4*x^3 + 10*x^4 - 28*x^5 + 76*x^6 - 184*x^7 + ...

Prog

(PARI) {a(n) = local(A, m); if( n<0, 0, m=1; A = 1 + O(x); while( m<=n, m*=2; A = (1 + 2*x) * subst(A, x, x^2 / (1 + 2*x)^2)); polcoeff(A, n))}

Crossrefs

Sequence in context: A132824 A298898 A339830 * A309159 A002420 A284016

Adjacent sequences: A078798 A078799 A078800 * A078802 A078803 A078804

Keyword

sign,easy

Author

Michael Somos, Dec 05 2002

Status

approved