A156340 - OEIS

%I #11 Oct 10 2020 11:16:24

%S 1,2,6,52,2150,423804,358766428,1257303170984,18016913850523398,

%T 1049450810327077624300,247590106794776589832254260,

%U 236013988752078034604114551553880,907420117150975291421488593816623266780,14052902173791695936955751957273562543384799320

%N G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2-n+1) * x^n/n ), a power series in x with integer coefficients.

%H Andrew Howroyd, <a href="/A156340/b156340.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = (1/n)*Sum_{k=1..n} 2^(k^2-k+1) * a(n-k) for n>0, with a(0)=1.

%F a(n) ~ 2^(n^2 - n + 1) / n. - _Vaclav Kotesovec_, Oct 07 2020

%e G.f.: A(x) = 1 + 2*x + 6*x^2 + 52*x^3 + 2150*x^4 + 423804*x^5 + ...

%e log(A(x)) = 2*x + 2^3*x^2/2 + 2^7*x^3/3 + 2^13*x^4/4 + 2^21*x^5/5 + 2^31*x^6/6 + ...

%o (PARI) {a(n)=polcoeff(exp(sum(k=1,n,2^(k^2-k+1)*x^k/k)+x*O(x^n)),n)}

%o for(n=0,15,print1(a(n),", "))

%o (PARI) {a(n)=if(n==0,1,(1/n)*sum(k=1,n,2^(k^2-k+1)*a(n-k)))}

%o for(n=0,15,print1(a(n),", "))

%Y Cf. A155200.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 08 2009

%E Terms a(12) and beyond from _Andrew Howroyd_, Jan 05 2020