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 A251588 #11 Sep 08 2022 08:46:10
%S A251588 1,1,10,254,11080,700008,58411696,6082359760,760774053888,
%T A251588 111229735731200,18626295180427264,3516652429787529216,
%U A251588 739238816214490808320,171262175332556483854336,43359709355122360320000000,11911510903698787868252045312,3529104034183977458725537447936,1121766516051874786454563454976000
%N A251588 a(n) = 8^(n-6) * (n+1)^(n-8) * (16807*n^6 + 143031*n^5 + 525875*n^4 + 1074745*n^3 + 1294846*n^2 + 876856*n + 262144).
%H A251588 G. C. Greubel, <a href="/A251588/b251588.txt">Table of n, a(n) for n = 0..296</a>
%F A251588 Let G(x) = 1 + x*G(x)^8 be the g.f. of A007556, then the e.g.f. A(x) of this sequence satisfies:
%F A251588 (1) A(x) = exp( 8*x*A(x) * G(x*A(x))^7 ) / G(x*A(x))^7.
%F A251588 (2) A(x) = F(x*A(x)) where F(x) = exp(8*x*G(x)^7)/G(x)^7 is the e.g.f. of A251578.
%F A251588 (3) a(n) = [x^n/n!] F(x)^(n+1)/(n+1) where F(x) is the e.g.f. of A251578.
%F A251588 E.g.f.: -LambertW(-8*x) * (8 + LambertW(-8*x))^7 / (x*8^8). - _Vaclav Kotesovec_, Dec 07 2014
%e A251588 E.g.f.: A(x) = 1 + x + 10*x^2/2! + 254*x^3/3! + 11080*x^4/4! + 700008*x^5/5! +...
%e A251588 such that A(x) = exp( 7*x*A(x) * G(x*A(x))^6 ) / G(x*A(x))^6
%e A251588 where G(x) = 1 + x*G(x)^8 is the g.f. of A007556:
%e A251588 G(x) = 1 + x + 8*x^2 + 92*x^3 + 1240*x^4 + 18278*x^5 + 285384*x^6 +...
%e A251588 RELATED SERIES.
%e A251588 Note that A(x) = F(x*A(x)) where F(x) = exp(8*x*G(x)^7)/G(x)^7,
%e A251588 F(x) = 1 + x + 8*x^2/2! + 176*x^3/3! + 6896*x^4/4! + 397888*x^5/5! +...
%e A251588 is the e.g.f. of A251578.
%t A251588 Table[8^(n - 6)*(n + 1)^(n - 8)*(16807*n^6 + 143031*n^5 + 525875*n^4 + 1074745*n^3 + 1294846*n^2 + 876856*n + 262144), {n, 0, 50}] (* _G. C. Greubel_, Nov 13 2017 *)
%o A251588 (PARI) {a(n) = 8^(n-6) * (n+1)^(n-8) * (16807*n^6 + 143031*n^5 + 525875*n^4 + 1074745*n^3 + 1294846*n^2 + 876856*n + 262144)}
%o A251588 for(n=0,20,print1(a(n),", "))
%o A251588 (PARI) {a(n) = local(G=1,A=1); for(i=1,n, G=1+x*G^8 +x*O(x^n));
%o A251588 for(i=1,n, A = exp(8*x*A * subst(G^7,x,x*A) ) / subst(G^7,x,x*A) ); n!*polcoeff(A, n)}
%o A251588 for(n=0, 20, print1(a(n), ", "))
%o A251588 (Magma) [8^(n - 6)*(n + 1)^(n - 8)*(16807*n^6 + 143031*n^5 + 525875*n^4 + 1074745*n^3 + 1294846*n^2 + 876856*n + 262144): n in [0..50]]; // _G. C. Greubel_, Nov 13 2017
%Y A251588 Cf. A251578, A007556.
%Y A251588 Cf. Variants: A251583, A251584, A251585, A251586, A251587, A251589, A251590.
%K A251588 nonn
%O A251588 0,3
%A A251588 _Paul D. Hanna_, Dec 06 2014