A296232 - OEIS

%I #13 Dec 22 2017 04:05:40

%S 1,1,7,154,7609,695856,103805719,23134327168,7227250033329,

%T 3017857024161280,1623903877812828871,1094152976804148581376,

%U 902056146753714911194537,892968703742747996041990144,1044915082876352591016398853975,1426374051728780629533978596663296,2245953139539256017165567029993025889

%N a(n) =  [x^n/n!] G(x)^((n+1)^2) / (n+1)^2 for n>=0, where G(x) is the e.g.f. of A296170.

%C E.g.f. G(x) of A296170 satisfies: [x^(n-1)] G(x)^(n^2) = [x^n] G(x)^(n^2) for n>=1.

%H Paul D. Hanna, <a href="/A296232/b296232.txt">Table of n, a(n) for n = 0..300</a>

%F a(n-1) = [x^n/n!] G(x)^(n^2) / n^2 for n>=1, where G(x) is the e.g.f. of A296170.

%F a(7*n) = 1 (mod 7) for n>=0.

%F a(7*n+2) = a(7*n+3) = a(7*n+4) = a(7*n+5) = 0 (mod 7) for n>=0.

%F a(n) ~ c * n^(2*n - 2), where c = 2.165959933... - _Vaclav Kotesovec_, Dec 20 2017

%o (PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^2)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^2 ); n!*polcoeff(Ser(A)^((n+1)^2)/((n+1)^2),n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A296170.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 08 2017