A265267 E.g.f.: exp(-2) * Sum_{n>=0} 2^n * (1+x)^(n^2) / n!.

1, 6, 88, 2160, 76336, 3594112, 214575872, 15695861760, 1371486918144, 140382841170944, 16572993648603136, 2228162239340027904, 337576082591565651968, 57121976918741964259328, 10713284121614206013898752, 2212342319434677836830015488, 500118162321472987555560620032, 123128345425943590420826294059008, 32864579386892803455158341264736256

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Example

E.g.f.: A(x) = 1 + 6*x + 88*x^2/2! + 2160*x^3/3! + 76336*x^4/4! + 3594112*x^5/5! + 214575872*x^6/6! + 15695861760*x^7/7! + 1371486918144*x^8/8! +...
where
A(x)*exp(2) = 1 + 2*(1+x) + 2^2*(1+x)^4/2! + 2^3*(1+x)^9/3! + 2^4*(1+x)^16/4! + 2^5*(1+x)^25/5! + 2^6*(1+x)^36/6! + 2^7*(1+x)^49/7! + 2^8*(1+x)^64/8! +...

Prog

(PARI) /* Quick print of terms 0..30: */
\p80
Vec(round( serlaplace( sum(n=0, 400, 2^n * (1+x +O(x^31))^(n^2) /n! *1.)/exp(2) ) ))

Crossrefs

Cf. A014507.

Sequence in context: A210005 A178296 A122770 * A218260 A177567 A177563

Adjacent sequences: A265264 A265265 A265266 * A265268 A265269 A265270

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2016

Status

approved