A351002 -id:A351002 - cp's OEIS frontend

A369494 a(n) = [x^(n(n+1)/2)] Product_{k=1..n} (x^(k(k+1)/2) + 1/x^(k*(k+1)/2)).

1, 1, 0, 0, 0, 2, 0, 3, 3, 5, 0, 14, 23, 39, 0, 101, 161, 315, 0, 971, 1595, 2872, 0, 9697, 17431, 31736, 0, 103608, 190242, 356883, 0, 1218049, 2235343, 4165201, 0, 14602056, 27304610, 51182196, 0, 179995388, 339041695, 640927871, 0, 2288387318, 4326722468, 8201714149

Offset: 0

Ilya Gutkovskiy, Jan 24 2024

nonn

Cf. A000217, A063890, A158380, A351002, A368243.

b:= proc(n, i) option remember; (m-> `if`(n>m, 0,
     `if`(n=m, 1, b(abs(n-i*(i+1)/2), i-1)+
        b(n+i*(i+1)/2, i-1))))((2+(3+i)*i)*i/6)
    end:
a:= n-> `if`(irem(n, 4)=2, 0, b(n*(n+1)/2, n)):
seq(a(n), n=0..45);  # Alois P. Heinz, Jan 24 2024

Table[Coefficient[Product[x^(k (k + 1)/2) + 1/x^(k (k + 1)/2), {k, 1, n}], x, n (n + 1)/2], {n, 0, 45}]

A369495 a(n) = [x^n] Product_{k=1..n} (x^(k(k+1)/2) + 1 + 1/x^(k(k+1)/2)).

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 11, 25, 56, 129, 313, 748, 1831, 4584, 11581, 29555, 76398, 199191, 522746, 1382158, 3676072, 9828631, 26412174, 71310248, 193346941, 526302232, 1437895915, 3941671019, 10839118898, 29893768219, 82671240995, 229213877639, 637049969282

Offset: 0

Ilya Gutkovskiy, Jan 24 2024

nonn

Cf. A000217, A316706, A351002, A369344, A369433.

b:= proc(n, i) option remember; (m-> `if`(n>m, 0,
     `if`(n=m, 1, b(abs(n-i*(i+1)/2), i-1)+b(n, i-1)+
        b(n+i*(i+1)/2, i-1))))((2+(3+i)*i)*i/6)
    end:
a:= n-> b(n$2):
seq(a(n), n=0..32);  # Alois P. Heinz, Jan 24 2024

Table[Coefficient[Product[x^(k (k + 1)/2) + 1 + 1/x^(k (k + 1)/2), {k, 1, n}], x, n], {n, 0, 32}]

cp's OEIS Frontend

A369494 a(n) = [x^(n(n+1)/2)] Product_{k=1..n} (x^(k(k+1)/2) + 1/x^(k*(k+1)/2)).

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A369495 a(n) = [x^n] Product_{k=1..n} (x^(k(k+1)/2) + 1 + 1/x^(k(k+1)/2)).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

cp's OEIS Frontend

A369494 a(n) = [x^(n*(n+1)/2)] Product_{k=1..n} (x^(k*(k+1)/2) + 1/x^(k*(k+1)/2)).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

A369495 a(n) = [x^n] Product_{k=1..n} (x^(k*(k+1)/2) + 1 + 1/x^(k*(k+1)/2)).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

A369494 a(n) = [x^(n(n+1)/2)] Product_{k=1..n} (x^(k(k+1)/2) + 1/x^(k*(k+1)/2)).

A369495 a(n) = [x^n] Product_{k=1..n} (x^(k(k+1)/2) + 1 + 1/x^(k(k+1)/2)).