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A167140 Self-convolution of A155200. 0

%I #2 Mar 30 2012 18:37:20

%S 1,4,24,416,34400,13561728,22961051392,160934805885952,

%T 4612329945733989888,537318814887463743641600,

%U 253532269357851227988228362240,483356648964255814869226601582346240

%N Self-convolution of A155200.

%F G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2+1)*x^n/n ).

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

%e G.f.: A(x) = 1 + 4*x + 24*x^2 + 416*x^3 + 34400*x^4 + 13561728*x^5 +...

%e A(x)^(1/2) = 1 + 2*x + 10*x^2 + 188*x^3 + 16774*x^4 + 6745436*x^5 +...

%e log(A(x)) = 2^2*x + 2^5*x^2/2 + 2^10*x^3/3 + 2^17*x^4/4 + 2^26*x^5/5 +...

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

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

%Y Cf. A155200.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 30 2009

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)