A301455 G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - x^k*A(x)^k)^k.

1, 1, 4, 16, 74, 360, 1840, 9698, 52409, 288697, 1615275, 9153850, 52434770, 303104532, 1765920785, 10358843904, 61129390652, 362650003202, 2161590275029, 12938838382316, 77745063802045, 468760264760369, 2835272729215565, 17198394229862818, 104598950726341920, 637709136315071504

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

G.f. A(x) satisfies: A(x) = exp(Sum_{k>=1} sigma_2(k)*x^k*A(x)^k/k).

Example

G.f. A(x) = 1 + x + 4*x^2 + 16*x^3 + 74*x^4 + 360*x^5 + 1840*x^6 + 9698*x^7 + 52409*x^8 + 288697*x^9 + ...
G.f. A(x) satisfies: A(x) = 1/((1 - x*A(x)) * (1 - x^2*A(x)^2)^2 * (1 - x^3*A(x)^3)^3 * ...).
log(A(x)) = x + 7*x^2/2 + 37*x^3/3 + 215*x^4/4 + 1251*x^5/5 + 7459*x^6/6 + 44885*x^7/7 + 272727*x^8/8 + ... + A255672(n)*x^n/n + ...

Crossrefs

Cf. A000219, A001157, A109085, A145268, A255672, A301456.

Sequence in context: A030131 A091530 A344248 * A214372 A366495 A109957

Adjacent sequences: A301452 A301453 A301454 * A301456 A301457 A301458

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 21 2018

Status

approved