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A357037 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6). 3
1, 0, 0, 1, 6, 35, 295, 3304, 42112, 599724, 9657330, 174222576, 3464835726, 75208002792, 1771121398956, 44998593873024, 1226723273550720, 35714547582173280, 1106012915718532920, 36304411160854523520, 1259105580819317636280, 46007354360033491345920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..21.

FORMULA

E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3 / 6.

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * |Stirling1(n,3*k)|/(6^k * k!).

MATHEMATICA

m = 22; (* number of terms *)

A[_] = 0;

Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^2/6) + O[x]^m // Normal, {m}];

CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)

PROG

(PARI) a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));

CROSSREFS

Cf. A001761, A357036.

Cf. A347002, A357029, A357032.

Sequence in context: A357095 A030446 A093989 * A356460 A261073 A261080

Adjacent sequences: A357034 A357035 A357036 * A357038 A357039 A357040

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 09 2022

STATUS

approved

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Last modified March 21 16:33 EDT 2023. Contains 361408 sequences. (Running on oeis4.)