cp's OEIS Frontend

A251671 a(n) = Sum_{k=0..n} C(n,k) * (2^k + 3^k)^k.

%I A251671 #10 Jan 25 2015 07:01:35
%S A251671 1,6,180,43398,88701816,1573206748746,248688444559874580,
%T A251671 356335498302585834118638,4663871943514788530035646937456,
%U A251671 558720685051192771669885091319459750546,612058892657175926094223171960469926874935754700
%N A251671 a(n) = Sum_{k=0..n} C(n,k) * (2^k + 3^k)^k.
%F A251671 G.f.: Sum_{n>=0} (2^n + 3^n)^n * x^n / (1-x)^(n+1).
%F A251671 a(n) ~ 3^(n^2). - _Vaclav Kotesovec_, Jan 25 2015
%e A251671 G.f.: A(x) = 1 + 6*x + 180*x^2 + 43398*x^3 + 88701816*x^4 + 1573206748746*x^5 +...
%e A251671 where A(x) = 1/(1-x) + (2+3)*x/(1-x)^2 + (2^2+3^2)*x^2/(1-x)^3 + (2^3+3^3)^3*x^3/(1-x)^4 +...
%e A251671 ILLUSTRATION OF INITIAL TERMS:
%e A251671 a(0) = 1*(2^0+3^0)^0 = 1;
%e A251671 a(1) = 1*(2^0+3^0)^0 + 1*(2^1+3^1)^1 = 6;
%e A251671 a(2) = 1*(2^0+3^0)^0 + 2*(2^1+3^1)^1 + 1*(2^2+3^2)^2 = 180;
%e A251671 a(3) = 1*(2^0+3^0)^0 + 3*(2^1+3^1)^1 + 3*(2^2+3^2)^2 + 1*(2^3+3^3)^3 = 43398;
%e A251671 a(4) = 1*(2^0+3^0)^0 + 4*(2^1+3^1)^1 + 6*(2^2+3^2)^2 + 4*(2^3+3^3)^3 + 1*(2^4+3^4)^4 = 88701816; ...
%t A251671 Table[Sum[Binomial[n,k] * (2^k + 3^k)^k,{k,0,n}],{n,0,15}] (* _Vaclav Kotesovec_, Jan 25 2015 *)
%o A251671 (PARI) {a(n)=sum(k=0, n, binomial(n, k) * (2^k + 3^k)^k )}
%o A251671 for(n=0, 15, print1(a(n), ", "))
%o A251671 (PARI) {a(n)=local(A=1); A=sum(m=0, n, (2^m + 3^m)^m * x^m / (1-x +x*O(x^n) )^(m+1) ); polcoeff(A, n)}
%o A251671 for(n=0, 15, print1(a(n), ", "))
%Y A251671 Cf. A251661, A251184, A060722.
%K A251671 nonn
%O A251671 0,2
%A A251671 _Paul D. Hanna_, Jan 21 2015