A227236 G.f.: Sum_{n>=0} x^n * (1+x)^sigma(n).

1, 1, 2, 4, 8, 15, 32, 64, 130, 300, 683, 1416, 2797, 5449, 10468, 20827, 48713, 140665, 440145, 1295627, 3366191, 7604954, 15054413, 26767480, 45010160, 78418102, 156829013, 367706520, 935824230, 2377653059, 5771777943, 13258948998, 29398875613, 66580469424, 167964244061

Offset

0,3

Comments

Here sigma(n) equals the sum of divisors of n (A000203).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 15*x^5 + 32*x^6 + 64*x^7 +...
where
A(x) = 1 + x*(1+x) + x^2*(1+x)^3 + x^3*(1+x)^4 + x^4*(1+x)^7 + x^5*(1+x)^6 + x^6*(1+x)^12 + x^7*(1+x)^8 + x^8*(1+x)^15 + x^9*(1+x)^13 + x^10*(1+x)^18 +...

Prog

(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*(1+x+x*O(x^n))^sigma(m)), n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A227237, A000203.

Sequence in context: A298533 A259805 A086125 * A061030 A036661 A145671

Adjacent sequences: A227233 A227234 A227235 * A227237 A227238 A227239

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2013

Status

approved