A293572 E.g.f.: exp(x/(1 + x + x^2 + x^3)).

1, 1, -1, -5, 1, 161, 31, -8021, -14335, 686881, 2925631, -91860229, -583959551, 15741408385, 169511794271, -3832934048789, -54596554106879, 1106568438159809, 23024933751472255, -412744343093399429, -11208399032299519999, 177909311974519181281

Offset: 0

Author

Seiichi Manyama, Oct 12 2017

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..446

Crossrefs

Cf. A111884, A293571, A293573.

Programs

Maple

f:= gfun:-rectoproc(n*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*a(n) + 2*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*a(n+1) + (n+5)*(n+4)*(n+3)*(8+3*n)*a(n+2) + (n+5)*(n+4)*(13+4*n)*a(n+3) + 3*(n+4)*(n+5)*a(n+4) + (9+2*n)*a(n+5) + a(n+6),
a(0) = 1, a(1) = 1, a(2) = -1, a(3) = -5, a(4) = 1, a(5) = 161}, a(n), remember):
map(f, [$0..25]); # Robert Israel, May 05 2020

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1+x+x^2+x^3))))

PARI

N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(4*k-3)-x^(4*k-2)))))

Formula

E.g.f.: Product_{k>0} exp(x^(4*k-3)) / exp(x^(4*k-2)).

n*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*a(n) + 2*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*a(n+1) + (n+5)*(n+4)*(n+3)*(8+3*n)*a(n+2) + (n+5)*(n+4)*(13+4*n)*a(n+3) + 3*(n+4)*(n+5)*a(n+4) + (9+2*n)*a(n+5) + a(n+6) = 0. - Robert Israel, May 05 2020