A326599 G.f.: Sum_{n>=0} x^n * (1 + x^n)^n / (1 - x*(1 + x^n))^(n+1).

1, 3, 8, 19, 44, 97, 207, 432, 884, 1777, 3529, 6942, 13547, 26281, 50791, 97942, 188677, 363489, 700953, 1354060, 2621602, 5088832, 9905382, 19335477, 37848971, 74287855, 146173721, 288280956, 569715036, 1127957956, 2236777539, 4441749653, 8830819362, 17574636239, 35005944165, 69776276002, 139165947494

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Example

G.f.: A(x) = 1 + 3*x + 8*x^2 + 19*x^3 + 44*x^4 + 97*x^5 + 207*x^6 + 432*x^7 + 884*x^8 + 1777*x^9 + 3529*x^10 + 6942*x^11 + 13547*x^12 + 26281*x^13 + ...
such that
A(x) = 1/(1-2*x) + x*(1+x)/(1 - x*(1+x))^2 + x^2*(1+x^2)^2/(1 - x*(1+x^2))^3 + x^3*(1+x^3)^3/(1 - x*(1+x^3))^4 + x^4*(1+x^4)^4/(1 - x*(1+x^4))^5  + x^5*(1+x^5)^5/(1 - x*(1+x^5))^6 + x^6*(1+x^6)^6/(1 - x*(1+x^6))^7 + ...

Prog

(PARI) {a(n) = my(A = sum(m=0, n, x^m * (1 + x^m +x*O(x^n))^m /(1 - x*(1+x^m)  +x*O(x^n))^(m+1) )); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A138247.

Sequence in context: A191787 A347310 A332719 * A121551 A189391 A281812

Adjacent sequences: A326596 A326597 A326598 * A326600 A326601 A326602

Keyword

nonn

Author

Paul D. Hanna, Jul 13 2019

Status

approved