A300615 O.g.f. A(x) satisfies: [x^n] exp( n^5 * A(x) ) = n^5 * [x^(n-1)] exp( n^5 * A(x) ) for n>=1.

1, 16, 19683, 142475264, 3436799053125, 212148041589128016, 28458158819417861315152, 7380230750280159370894934016, 3385049575573746853297963891959753, 2561548157856026756893458765378989150000, 3026444829408778969259555715061437179090541565, 5340113530831632053993990154143996936096662034267136

Offset: 1

Author

Paul D. Hanna, Mar 10 2018

Keywords

• nonn

Comments

Compare to: [x^n] exp( n^5 * x ) = n^4 * [x^(n-1)] exp( n^5 * x ) for n>=1.

Examples

			O.g.f.: A(x) = x + 16*x^2 + 19683*x^3 + 142475264*x^4 + 3436799053125*x^5 + 212148041589128016*x^6 + 28458158819417861315152*x^7 + ...
where
exp(A(x)) = 1 + x + 33*x^2/2! + 118195*x^3/3! + 3419881993*x^4/4! + 412433022394701*x^5/5! + 152749066271797582081*x^6/6! + ... + A300614(n)*x^n/n! + ...
such that: [x^n] exp( n^5 * A(x) ) = n^5 * [x^(n-1)] exp( n^5 * A(x) ).
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A300614, A296171, A300591, A300593, A300595, A300597.

Programs

PARI

{a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^5)); A[#A] = ((#A-1)^5*V[#A-1] - V[#A])/(#A-1)^5 ); polcoeff( log(Ser(A)), n)}
for(n=1, 20, print1(a(n), ", "))

Formula

O.g.f. equals the logarithm of the e.g.f. of A300614.