A368478 a(n) = [x^n] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 22, 88, 236, 568, 1147, 1999, 3030, 4333, 4793, 5620, 4628, 9353, 40048, 312436, 1638550, 7894061, 30866741, 105342660, 323671449, 863529149, 2152428536, 4750103818, 9796453345, 18572505806, 32181800057, 55712628236

Offset

0,13

Links

Table of n, a(n) for n=0..38.

Maple

b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1, b(n, i-1)+
      b(abs(n-i^4), i-1)+b(n+i^4, i-1))))(i*(i+1)*(2*i+1)*(3*i^2+3*i-1)/30)
    end:
a:= n-> b(n$2):
seq(a(n), n=0..33);  # Alois P. Heinz, Jan 25 2024

Crossrefs

Cf. A000583, A316706, A369358, A369433, A369437.

Sequence in context: A135836 A004305 A275290 * A277228 A302272 A302723

Adjacent sequences: A368475 A368476 A368477 * A368479 A368480 A368481

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 25 2024

Extensions

a(34)-a(38) from Alois P. Heinz, Jan 25 2024

Status

approved