A299437 G.f.: exp( Sum_{n>=1} A020696(n)/2 * x^n/n ), where A020696(n) = Product_{d|n} (d + 1).

1, 1, 2, 3, 7, 9, 27, 33, 73, 100, 203, 269, 987, 1163, 2283, 3234, 6706, 8812, 21455, 27211, 55718, 76055, 147048, 196483, 533149, 659549, 1262531, 1759301, 3462333, 4593487, 10261739, 13213278, 25944342, 35397849, 66694451, 89412873, 209286231, 266115126, 499426529, 689936238, 1311854563, 1750578063, 3676669661, 4787587399, 9114353938, 12427479022, 22925519170

Offset

0,3

Comments

Self-convolution equals A299436.

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 7*x^4 + 9*x^5 + 27*x^6 + 33*x^7 + 73*x^8 + 100*x^9 + 203*x^10 + 269*x^11 + 987*x^12 + 1163*x^13 + 2283*x^14 + ...
such that
log(A(x)) = x + 3*x^2/2 + 4*x^3/3 + 15*x^4/4 + 6*x^5/5 + 84*x^6/6 + 8*x^7/7 + 135*x^8/8 + 40*x^9/9 + 198*x^10/10 + 12*x^11/11 + 5460*x^12/12 + 14*x^13/13 + 360*x^14/14 + 384*x^15/15 + ... + A020696(n)/2*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)/2*x^m/m ) +x*O(x^n) )); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A299436 (A(x)^2), A020696.

Sequence in context: A333517 A207643 A205488 * A255393 A248037 A123481

Adjacent sequences: A299434 A299435 A299436 * A299438 A299439 A299440

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2018

Status

approved