A296232 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.

1, 1, 7, 154, 7609, 695856, 103805719, 23134327168, 7227250033329, 3017857024161280, 1623903877812828871, 1094152976804148581376, 902056146753714911194537, 892968703742747996041990144, 1044915082876352591016398853975, 1426374051728780629533978596663296, 2245953139539256017165567029993025889

Offset

0,3

Comments

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

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Formula

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.

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

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

a(n) ~ c * n^(2*n - 2), where c = 2.165959933... - Vaclav Kotesovec, Dec 20 2017

Prog

(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)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A296170.

Sequence in context: A213113 A144683 A229711 * A279662 A214382 A141835

Adjacent sequences: A296229 A296230 A296231 * A296233 A296234 A296235

Keyword

nonn

Author

Paul D. Hanna, Dec 08 2017

Status

approved