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A393852
O.g.f. A(x) satisfies: [x^n] exp( n^5*x - n^2*A(x) ) = 0 for n >= 1.
6
1, 98, 214344, 2422736288, 86404408885000, 7522353279784847520, 1361020067428146706895552, 457729018890814234481125167104, 263558187228906049449501760761461088, 243920083465149722342720826648941363212800, 345154327291523887411720506126476368087604332352, 717088358317356048916029332387642017554036276257129472
OFFSET
1,2
LINKS
EXAMPLE
O.g.f.: A(x) = x + 98*x^2 + 214344*x^3 + 2422736288*x^4 + 86404408885000*x^5 + 7522353279784847520*x^6 + ...
ILLUSTRATION OF DEFINITION.
The table of coefficients of x^k/k! in exp( n^5*x - n^2*A(x) ) begins
n = 1: [1, 0, -196, -1286064, ...];
n = 2: [1, 28, 0, -5188160, ...];
n = 3: [1, 234, 52992, 0, ...];
n = 4: [1, 1008, 1012928, 994132224, 0, ...];
n = 5: [1, 3100, 9605100, 29713278400, 90217316417200, 0, ...]; ...
in which a diagonal, the coefficient of x^n in row n, is all zeros.
RELATED SERIES.
exp(A(x)) = 1 + x + 197*x^2/2! + 1286653*x^3/3! + 58150931593*x^4/4! + 10368822328678841*x^5/5! + 5416156760994815588941*x^6/6! + ...
where [x^n] exp(n^5*x) / exp(A(x))^(n^2) = 0 for n >= 1.
PROG
(PARI) {a(n, p=5, q=2) = my(A=[0], m); for(i=1, n+1, m=#A; A=concat(A, 0); A[m+1] = Vec( exp(m^p*x - m^q*Ser(A)) )[m+1]/(m^q) ); polcoef( Ser(A), n)}
for(n=1, 15, print1(a(n, 5, 2), ", "))
CROSSREFS
Below, sequences with the parameters (p,q) indicated have an o.g.f. F(x) satisfying [x^n] exp( n^p*x - n^q*F(x) ) = 0 for n >= 1.
Cf. A319944 (5,1), A393853 (5,3), A393854 (5,4).
Cf. A317346 (3,2), A319942 (4,2), A393862 (6,2), A393872 (7,2), A393882 (8,2).
Sequence in context: A146199 A159381 A295191 * A295184 A295186 A097601
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 02 2026
STATUS
approved