A299436 G.f.: exp( Sum_{n>=1} A020696(n) * x^n/n ), where A020696(n) = Product_{d|n} (d + 1).

1, 2, 5, 10, 24, 44, 109, 198, 423, 766, 1555, 2730, 6269, 11090, 22127, 39246, 77541, 134242, 270348, 467004, 895797, 1546922, 2905899, 4943126, 9666435, 16471506, 30604583, 52206218, 96412319, 162467222, 303289098, 510436808, 929735638, 1564811464, 2818065892, 4700325864, 8619686709, 14378564170, 25693238857, 42876196186, 76267527522, 126317457712

Offset

0,2

Comments

Self-convolution of A299437.

Links

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

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 10*x^3 + 24*x^4 + 44*x^5 + 109*x^6 + 198*x^7 + 423*x^8 + 766*x^9 + 1555*x^10 + 2730*x^11 + 6269*x^12 + 11090*x^13 + ...
such that
log(A(x)) = 2*x + 6*x^2/2 + 8*x^3/3 + 30*x^4/4 + 12*x^5/5 + 168*x^6/6 + 16*x^7/7 + 270*x^8/8 + 80*x^9/9 + 396*x^10/10 + 24*x^11/11 + 10920*x^12/12 + 28*x^13/13 + 720*x^14/14 + 768*x^15/15 + ... + A020696(n)*x^n/n + ...

Prog

(PARI) A020696(n) = {d = divisors(n); return (prod(i=1, #d, d[i]+1)); } \\ after Michel Marcus
{a(n) = my(A = exp( sum(m=1, n, A020696(m)*x^m/m ) +x*O(x^n) )); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A299437 (sqrt(A(x))), A020696.

Sequence in context: A152784 A112855 A361505 * A049937 A026754 A291247

Adjacent sequences: A299433 A299434 A299435 * A299437 A299438 A299439

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2018

Status

approved