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A356914
E.g.f. satisfies: A(x) = 1/(1 - x * A(x)^2)^A(x).
2
1, 1, 8, 129, 3188, 106820, 4530174, 232744274, 14054237000, 975665799792, 76568358325440, 6703512043934112, 647772783078516600, 68484470168404178928, 7863452609057425825704, 974474039841523412062440, 129636661193226128284609344, 18427094124309886080021680640
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (2*n+k+1)^(k-1) * |Stirling1(n,k)|.
MATHEMATICA
m = 18; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x]^2)^A[x] + 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, (2*n+k+1)^(k-1)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 07 2022
STATUS
approved