A156340 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2-n+1) * x^n/n ), a power series in x with integer coefficients.

1, 2, 6, 52, 2150, 423804, 358766428, 1257303170984, 18016913850523398, 1049450810327077624300, 247590106794776589832254260, 236013988752078034604114551553880, 907420117150975291421488593816623266780, 14052902173791695936955751957273562543384799320

Offset: 0

Author

Paul D. Hanna, Feb 08 2009

Keywords

• nonn

Examples

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A155200.

Programs

PARI

{a(n)=polcoeff(exp(sum(k=1,n,2^(k^2-k+1)*x^k/k)+x*O(x^n)),n)}
for(n=0,15,print1(a(n),", "))

PARI

{a(n)=if(n==0,1,(1/n)*sum(k=1,n,2^(k^2-k+1)*a(n-k)))}
for(n=0,15,print1(a(n),", "))

Formula

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

a(n) ~ 2^(n^2 - n + 1) / n. - Vaclav Kotesovec, Oct 07 2020

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 05 2020