A182349 - OEIS

%I #6 Aug 11 2021 12:12:10

%S 1,6,30,120,435,1446,4536,13560,39045,108950,296178,787368,2053335,

%T 5265750,13306380,33188040,81815145,199585830,482290630,1155444120,

%U 2746489851,6481600326,15195437280,35407315800,82038719565,189089191926,433704632346,990244936520

%N G.f.: exp( Sum_{n>=1} 6 * A084214(n) * x^n/n ) where g.f. of A084214 is (1+x^2)/((1+x)*(1-2*x)).

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (6,-6,-24,39,42,-72,-48,48,32).

%F G.f.: 1/((1+x)^4*(1-2*x)^5).

%e G.f.: A(x) = 1 + 6*x + 30*x^2 + 120*x^3 + 435*x^4 + 1446*x^5 + 4536*x^6 +...

%e such that

%e log(A(x))/6 = x + 4*x^2/2 + 6*x^3/3 + 14*x^4/4 + 26*x^5/5 + 54*x^6/6 + 106*x^7/7 + 214*x^8/8 +...+ A084214(n) * x^n/n +...

%t CoefficientList[Series[1/((1+x)^4(1-2x)^5),{x,0,30}],x] (* or *) LinearRecurrence[{6,-6,-24,39,42,-72,-48,48,32},{1,6,30,120,435,1446,4536,13560,39045},30] (* _Harvey P. Dale_, Aug 11 2021 *)

%o (PARI) {A084214(n)=polcoeff((1+x^2)/((1+x)*(1-2*x+x*O(x^n))), n)}

%o {a(n)=polcoeff(exp(sum(k=1, n, 6*A084214(k)*x^k/k)+x*O(x^n)), n)}

%o for(n=0, 16, print1(a(n), ", "))

%Y Cf. A084214.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 25 2012