A322739 - OEIS

A322739

E.g.f. A(x) satisfies: A(x) = Sum_{n>=0} ( exp(2*n*x) - A(x)^n )^n.

1, 1, 6, 97, 3708, 286126, 36084756, 6508298392, 1561731069408, 477312184046536, 180343755827049456, 82394590229211894712, 44740419997671632176608, 28473068297755201366432096, 20991426702927285864685894656, 17750540113634768604238519234432, 17068843562200262650028592424055808, 18523905645979169633858014762594493056, 22535986879713040510351902189004731737856, 30550606589946151569429508183181183877223552

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

EXAMPLE

E.g.f.: A(x) = 1 + x + 6*x^2/2! + 97*x^3/3! + 3708*x^4/4! + 286126*x^5/5! + 36084756*x^6/6! + 6508298392*x^7/7! + 1561731069408*x^8/8! + 477312184046536*x^9/9! + 180343755827049456*x^10/10! + ...

such that

A(x) = 1 + (exp(2*x) - A(x)) + (exp(4*x) - A(x)^2)^2 + (exp(6*x) - A(x)^3)^3 + (exp(8*x) - A(x)^4)^4 + (exp(10*x) - A(x)^5)^5 + (exp(12*x) - A(x)^6)^6 + ...

PROG

(PARI) {a(n) = my(A=[1]); for(i=1, n,

A=concat(A, 0); A=(A+Vec(sum(n=0, #A, (exp(2*x +x*O(x^#A))^n - Ser(A)^n)^n)))/2 ); n!*A[n+1]}

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

CROSSREFS

Sequence in context: A285025 A288544 A064753 * A244251 A187522 A224615

Adjacent sequences: A322736 A322737 A322738 * A322740 A322741 A322742

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 12 2019

STATUS

approved