A262842 G.f.: Product_{k>=1} (1 - x^k)^(-k^(k-2)).

1, 1, 2, 5, 22, 150, 1469, 18452, 282426, 5088276, 105431378, 2469403421, 64508609896, 1859464257187, 58625171707730, 2006861834895431, 74128128916520263, 2938711927441481562, 124457492116819509679, 5607967808192795374759, 267883606645817181302028, 13522287374792657280601627, 719232962773594118661491002, 40204966834965724305054746851

Offset: 0

Author

Paul D. Hanna, Oct 03 2015

Keywords

• nonn

Examples

			 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 22*x^4 + 150*x^5 + 1469*x^6 +...
where
A(x) = 1/((1-x)*(1-x^2)*(1-x^3)^3*(1-x^4)^16*(1-x^5)^125*(1-x^6)^1296*...)
also
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 67*x^4/4 + 626*x^5/5 + 7788*x^6/6 + 117650*x^7/7 + 2097219*x^8/8 + 43046731*x^9/9 + 1000000628*x^10/10 +...+ A262843(n)*x^n/n +...
		

Crossrefs

Cf. A262843, A023879.

Programs

PARI

{a(n)=polcoeff(prod(k=1, n, (1 - x^k +x*O(x^n))^(-k^(k-2))), n)}
for(n=0,30,print1(a(n),", "))

PARI

{a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, d^d)*x^m/m) +x*O(x^n)), n)}
for(n=0,30,print1(a(n),", "))

Formula

G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} d^(d-1) ).

Logarithmic derivative equals A262843, where A262843(n) = Sum_{d|n} d^(d-1).