A296175 G.f. equals the logarithm of the e.g.f. of A296174.

1, -7, -493, -341101, -680813601, -2923660883625, -22996362478599551, -299331006952284448127, -6006951481145880962408552, -176288642409787912257773903552, -7260231964238768891891716773249396, -405879958110794676900559524931590299892, -29968312587171485511980894312242331299164248, -2855987647850204274493781603297327940940773633392

Offset

1,2

Comments

E.g.f. G(x) of A296174 satisfies: [x^(n-1)] G(x)^(n^4) = [x^n] G(x)^(n^4) for n>=1.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..160

Formula

a(n) ~ -sqrt(1-c) * 2^(8*n - 17/2) * n^(3*n - 9/2) / (sqrt(Pi) * c^n * (4-c)^(3*n - 4) * exp(3*n)), where c = -LambertW(-4*exp(-4)) = 0.07930960512711365643910864... - Vaclav Kotesovec, Oct 13 2020

Example

G.f. A(x) = x - 7*x^2 - 493*x^3 - 341101*x^4 - 680813601*x^5 - 2923660883625*x^6 - 22996362478599551*x^7 - 299331006952284448127*x^8 - 6006951481145880962408552*x^9 - 176288642409787912257773903552*x^10 - 7260231964238768891891716773249396*x^11 - 405879958110794676900559524931590299892*x^12 +...
such that
G(x) = exp(A(x)) = 1 + x - 13*x^2/2! - 2999*x^3/3! - 8197751*x^4/4! - 81738176899*x^5/5! - 2105524335759389*x^6/6! - 115916378979693710123*x^7/7! - 12069952631345502122877199*x^8/8! - 2179911119857340269414590758951*x^9/9! - 639738016495616440994202167765715629*x^10/10! +...
satisfies [x^(n-1)] G(x)^(n^4) = [x^n] G(x)^(n^4) for n>=1.
Series_Reversion(A(x)) = x + 7*x^2 + 591*x^3 + 360071*x^4 + 696409901*x^5 + 2958728428011*x^6 + 23164541753169117*x^7 + 300801581861406441263*x^8 +...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^4)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^4 ); polcoeff(log(Ser(A)), n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A296174, A296171, A296173, A296177.

Sequence in context: A142734 A120773 A116167 * A319831 A122523 A293180

Adjacent sequences: A296172 A296173 A296174 * A296176 A296177 A296178

Keyword

sign

Author

Paul D. Hanna, Dec 07 2017

Status

approved