A265267 - OEIS

%I #6 Oct 30 2024 21:08:20

%S 1,6,88,2160,76336,3594112,214575872,15695861760,1371486918144,

%T 140382841170944,16572993648603136,2228162239340027904,

%U 337576082591565651968,57121976918741964259328,10713284121614206013898752,2212342319434677836830015488,500118162321472987555560620032,123128345425943590420826294059008,32864579386892803455158341264736256

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

%e 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! +...

%e where

%e 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! +...

%o (PARI) /* Quick print of terms 0..30: */

%o \p80

%o Vec(round( serlaplace( sum(n=0,400, 2^n * (1+x +O(x^31))^(n^2) /n! *1.)/exp(2) ) ))

%Y Cf. A014507.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 04 2016