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URL: https://oeis.org/A393849

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A393849
O.g.f. A(x) satisfies: [x^n] exp( n^9 * x ) / A(x) = 0 for n>0.
5
1, 1, 130561, 1268169652561, 196425341268811084961, 236460748444613412476233431261, 1452512207249667088850630689473004727833, 34514894930017989773911751736662931844960439257485, 2607266146824546128860167896833420117295169393153414445955457
OFFSET
0,3
LINKS
EXAMPLE
O.g.f.: A(x) = 1 + x + 130561*x^2 + 1268169652561*x^3 + 196425341268811084961*x^4 + 236460748444613412476233431261*x^5 + ...
ILLUSTRATION OF DEFINITION.
The table of coefficients of x^k/k! in exp(n^9*x)/A(x) begins
n = 1: [1, 0, -261121, -7609017132002, ...];
n = 2: [1, 511, 0, -7609283997664, ...];
n = 3: [1, 19682, 387120003, 0, ...];
n = 4: [1, 262143, 68718691328, 18006377981579296, 0, ...];
n = 5: [1, 1953124, 3814693098255, 7450560013815682610, 14547105795912570137404925, 0, ...];
...
in which a diagonal, the coefficient of x^n in row n, is all zeros.
PROG
(PARI) {a(n, k=9) = my(A=[1]); for(i=1, n, A=concat(A, 0); m=#A; A[m] = Vec( exp(x*(m-1)^k +x*O(x^m)) / Ser(A) )[m] ); A[n+1]}
for(n=0, 15, print1( a(n, 9), ", "))
CROSSREFS
Sequences below with the given parameter p have an o.g.f. F(x) satisfying [x^n] exp( n^p*x ) / F(x) = 0 for n >= 1.
Cf. A304322 (p=2), A304323 (p=3), A304324 (p=4), A304325 (p=5).
Cf. A393846 (p=6), A393847 (p=7), A393848 (p=8).
Sequence in context: A225026 A202935 A013893 * A013693 A103534 A239610
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 02 2026
STATUS
approved