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A295813 G.f. A(x) satisfies: G(A(x)) = exp(x), where G(x) equals the e.g.f. of A296172. 4
1, 3, 48, 3271, 575163, 185377116, 93039467356, 66505075585875, 63970743282062646, 79580632411431634441, 124299284968805234137968, 238188439678208173206500760, 549611050835556942751087049225, 1503700734638162443238902233252144, 4814751647416985610768723994195186728, 17841762828286483988438913318683740082187, 75777421917902616009655480827109144353730842 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

E.g.f. G(x) of A296172 satisfies: [x^(n-1)] G(x)^(n^3) = [x^n] G(x)^(n^3) for n>=1.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..200

FORMULA

G.f. is the series reversion of the logarithm of the e.g.f. of A296172.

EXAMPLE

G.f.: A(x) = x + 3*x^2 + 48*x^3 + 3271*x^4 + 575163*x^5 + 185377116*x^6 + 93039467356*x^7 + 66505075585875*x^8 + 63970743282062646*x^9 + 79580632411431634441*x^10 + 124299284968805234137968*x^11 + 238188439678208173206500760*x^12 +...

The series reversion equals the logarithm of the e.g.f. of A296172, which begins:

Series_Reversion(A(x)) = x - 3*x^2 - 30*x^3 - 2686*x^4 - 517311*x^5 - 173118807*x^6 - 88535206152*x^7 - 63977172334344*x^8 - 61971659588102940*x^9 - 77470793599569049440*x^10 - 121439997599825393413344*x^11 - 233353875172602479932391040*x^12 +...+ A296173(n)*x^n +...

PROG

(PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^3)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^3 ); polcoeff(serreverse(log(Ser(A))), n)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Cf. A296172, A296173, A295812, A295814.

Sequence in context: A304208 A300871 A201698 * A326217 A003029 A049524

Adjacent sequences:  A295810 A295811 A295812 * A295814 A295815 A295816

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 09 2017

STATUS

approved

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Last modified March 30 10:26 EDT 2020. Contains 333125 sequences. (Running on oeis4.)