A167140 Self-convolution of A155200.

1, 4, 24, 416, 34400, 13561728, 22961051392, 160934805885952, 4612329945733989888, 537318814887463743641600, 253532269357851227988228362240, 483356648964255814869226601582346240

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

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

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

Example

G.f.: A(x) = 1 + 4*x + 24*x^2 + 416*x^3 + 34400*x^4 + 13561728*x^5 +...
A(x)^(1/2) = 1 + 2*x + 10*x^2 + 188*x^3 + 16774*x^4 + 6745436*x^5 +...
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 +...

Prog

(PARI) {a(n)=polcoeff(exp( 2*sum(k=1, n, 2^(k^2)*x^k/k)+x*O(x^n)), n)}
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, 2^(k^2+1)*a(n-k)))}

Crossrefs

Cf. A155200.

Sequence in context: A196687 A185457 A024250 * A010572 A247737 A326871

Adjacent sequences: A167137 A167138 A167139 * A167141 A167142 A167143

Keyword

nonn

Author

Paul D. Hanna, Oct 30 2009

Status

approved