A208816 G.f.: Sum_{n>=0} Product_{k=1..n} ((1+2*x)^k - 1)/((1+2*x)^k + 1).

1, 1, 1, 3, 9, 39, 193, 1135, 7585, 57055, 476161, 4366399, 43627393, 471693439, 5486186497, 68296367871, 906012795393, 12758750871039, 190081374027777, 2986828127798271, 49367131036252161, 856162355062638591, 15545263081776742401, 294905583408022810623

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..340

Formula

a(n) ~ c * 8^n * n^(n+1) / (exp(n) * Pi^(2*n)), where c = 16*sqrt(2) / (Pi^2 * exp(Pi^2/8)) = 0.6676454503392449294235... . - Vaclav Kotesovec, Nov 06 2014, updated Aug 22 2017

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 9*x^4 + 39*x^5 + 193*x^6 + 1135*x^7 + ...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, ((1+2*x)^k - 1)/((1+2*x)^k + 1 +x*O(x^n)))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A287063 A080635 A278749 * A130905 A030799 A273396

Adjacent sequences: A208813 A208814 A208815 * A208817 A208818 A208819

Keyword

nonn

Author

Paul D. Hanna, Mar 01 2012

Status

approved