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URL: https://oeis.org/A393846

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A393846
O.g.f. A(x) satisfies: [x^n] exp( n^6 * x ) / A(x) = 0 for n>0.
5
1, 1, 1985, 62861994, 11442690973075, 7570836550478960487, 13956629370284243750857868, 60197488880602894559278221637956, 536790646696527838745317223865162477075, 9023894622972758071209681557435066872979358504
OFFSET
0,3
LINKS
EXAMPLE
O.g.f.: A(x) = 1 + x + 1985*x^2 + 62861994*x^3 + 11442690973075*x^4 + 7570836550478960487*x^5 + 13956629370284243750857868*x^6 + ...
ILLUSTRATION OF DEFINITION.
The table of coefficients of x^k/k! in exp(n^6*x)/A(x) begins
n = 1: [1, 0, -3969, -377160056, ...];
n = 2: [1, 63, 0, -377660150, ...];
n = 3: [1, 728, 526015, 0, ...];
n = 4: [1, 4095, 16765056, 68243238154, 0, ...];
n = 5: [1, 15624, 244105407, 3813401695600, 59285380255397541, 0, ...];
...
in which a diagonal, the coefficient of x^n in row n, is all zeros.
PROG
(PARI) {a(n, k=6) = 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, 6), ", "))
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. A393847 (p=7), A393848 (p=8), A393849 (p=9).
Sequence in context: A107527 A034228 A028516 * A376831 A206363 A233712
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 02 2026
STATUS
approved