This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229260 #14 Nov 10 2017 18:24:12
%S A229260 1,1,33,4759,1812645,1432421311,2033196095973,4707913008727279,
%T A229260 16598602853910799125,84603008117292025844671,
%U A229260 598699398082553327852353413,5694542805400507375406964870799,70891082687197321771955383523878005,1129717853570486718325946169950885995231
%N A229260 O.g.f.: Sum_{n>=0} n! * n^(2*n) * x^n / Product_{k=1..n} (1 - n^2*k*x).
%H A229260 G. C. Greubel, <a href="/A229260/b229260.txt">Table of n, a(n) for n = 0..160</a>
%F A229260 a(n) = Sum_{k=0..n} k^(2*n) * k! * Stirling2(n, k).
%F A229260 E.g.f.: Sum_{n>=0} (exp(n^2*x) - 1)^n.
%F A229260 a(n) ~ c * d^n * (n!)^3 / n, where d = r^3*(1+exp(2/r)) = 7.8512435106631367719817991716164612615296980032514..., r = 0.94520217245242431308104743874492469552738... is the root of the equation (1+exp(-2/r))*LambertW(-exp(-1/r)/r) = -1/r, and c = 0.142680262107781025906560380273234930916319644... . - _Vaclav Kotesovec_, May 08 2014
%e A229260 O.g.f.: A(x) = 1 + x + 33*x^2 + 4759*x^3 + 1812645*x^4 + 1432421311*x^5 +...
%e A229260 where
%e A229260 A(x) = 1 + x/(1-x) + 2!*2^4*x^2/((1-2^2*1*x)*(1-2^2*2*x)) + 3!*3^6*x^3/((1-3^2*1*x)*(1-3^2*2*x)*(1-3^2*3*x)) + 4!*4^8*x^4/((1-4^2*1*x)*(1-4^2*2*x)*(1-4^2*3*x)*(1-4^2*4*x)) +...
%e A229260 Exponential Generating Function.
%e A229260 E.g.f.: E(x) = 1 + x + 33*x^2/2! + 4759*x^3/3! + 1812645*x^4/4! +...
%e A229260 where
%e A229260 E(x) = 1 + (exp(x)-1) + (exp(4*x)-1)^2 + (exp(9*x)-1)^3 + (exp(16*x)-1)^4 + (exp(25*x)-1)^5 + (exp(36*x)-1)^6 + (exp(49*x)-1)^7 +...
%t A229260 Flatten[{1,Table[Sum[k^(2*n) * k! * StirlingS2[n,k], {k,0,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, May 08 2014 *)
%o A229260 (PARI) {a(n)=polcoeff(sum(m=0,n,m!*m^(2*m)*x^m/prod(k=1,m,1-m^2*k*x +x*O(x^n))),n)}
%o A229260 for(n=0,20,print1(a(n),", "))
%o A229260 (PARI) {a(n)=n!*polcoeff(sum(m=0,n,(exp(m^2*x+x*O(x^n))-1)^m),n)}
%o A229260 for(n=0,20,print1(a(n),", "))
%o A229260 (PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
%o A229260 {a(n)=sum(k=0, n, k^(2*n) * k! * Stirling2(n, k))}
%o A229260 for(n=0,20,print1(a(n),", "))
%Y A229260 Cf. A229257, A229258, A229259, A229261, A229233, A229234, A220181, A122399.
%Y A229260 Cf. A187755.
%K A229260 nonn
%O A229260 0,3
%A A229260 _Paul D. Hanna_, Sep 17 2013