A319143 G.f. A(x) satisfies: [x^(n-1)] (1+x)^(n^3) / A(x)^(n^2) = 0 for n>1.

1, 2, 5, 190, 24444, 6189050, 2551526428, 1545212826174, 1288051774444110, 1412705106844118046, 1971892031185697252554, 3413903325218336008192250, 7181500581229611492081984526, 18048175081484797766245697300090, 53425898749319275351535742806432314, 184046820557885265127311961578368691278, 730192327635057505047728578528016106455194

Offset: 0

Author

Paul D. Hanna, Sep 18 2018

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 5*x^2 + 190*x^3 + 24444*x^4 + 6189050*x^5 + 2551526428*x^6 + 1545212826174*x^7 + 1288051774444110*x^8 + ...
The table of coefficients of x^k in (1+x)^(n^3) / A(x)^(n^2) begins:
n=1: [1, -1, -3, -179, -23881, -6115379, -2532879873, ...];
n=2: [1, 0, -16, -728, -96144, -24548304, -10154627640, ...];
n=3: [1, 9, 0, -1878, -231876, -57206466, -23347565964, ...];
n=4: [1, 32, 432, 0, -472008, -111871136, -43940424080, ...];
n=5: [1, 75, 2675, 55475, 0, -199916560, -76768966500, ...];
n=6: [1, 144, 10152, 460056, 13896684, 0, -126293662512, ...];
n=7: [1, 245, 29694, 2364152, 137272471, 5735706025, 0, ...]; ...
in which the n-th term in row n forms a diagonal of zeros after an initial '1'.
		

Crossrefs

Cf. A303060.

Programs

PARI

{a(n) = my(A=[1]); for(m=1,n+1, A=concat(A,0); A[m] = Vec( (1+x +x*O(x^n))^(m^3)/Ser(A)^(m^2) )[m]/m^2 ); A[n+1]}
for(n=0,30, print1(a(n),", "))