A350738 -id:A350738 - cp's OEIS frontend

A350310 Alternating row sums of A066448.

1, -1, -2, -2, -1, 0, 2, 4, 6, 7, 8, 8, 6, 4, 0, -6, -11, -18, -26, -32, -38, -44, -46, -46, -44, -37, -26, -12, 8, 32, 58, 90, 124, 158, 194, 228, 259, 286, 306, 316, 316, 304, 276, 232, 170, 88, -12, -132, -272, -431, -606, -794, -994, -1200, -1408, -1614, -1808, -1984, -2138, -2258, -2336

Offset: 0

Seiichi Manyama, Jan 12 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A039924, A066447, A066448, A237979, A350737, A350738.

my(N=66, x='x+O('x^N)); Vec(sum(k=0, sqrtint(N), (-1)^k*x^k^2*prod(j=1, k, (1+x^j)/(1-x^j))))

a(n) = Sum_{k=0..n} (-1)^k * A066448(n,k).

G.f.: Sum_{k>=0} (-1)^k * x^(k^2) * Product_{j=1..k} (1+x^j)/(1-x^j).

A350737 Expansion of Sum_{k>=0} (-1)^k * x^(k(3k+1)/2) / Product_{j=1..k} (1-x^j).

Original entry on oeis.org

1, 0, -1, -1, -1, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 2, 1, 0, -1, -2, -4, -5, -6, -8, -9, -10, -11, -12, -12, -13, -12, -12, -11, -10, -7, -6, -3, 0, 4, 7, 12, 15, 21, 25, 30, 34, 40, 43, 48, 51, 55, 56, 59, 59, 60, 58, 56, 52, 49, 42, 35, 26, 17, 5, -7, -21, -36, -52, -69, -87, -105, -124, -144, -163

Offset: 0

Seiichi Manyama, Jan 12 2022

sign

Cf. A039924, A237979, A350310, A350738.

my(N=99, x='x+O('x^N)); Vec(sum(k=0, N, (-1)^k*x^(k*(3*k+1)/2)/prod(j=1, k, 1-x^j)))

cp's OEIS Frontend

A350310 Alternating row sums of A066448.

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A350737 Expansion of Sum_{k>=0} (-1)^k * x^(k(3k+1)/2) / Product_{j=1..k} (1-x^j).

Views

Author

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PARI

cp's OEIS Frontend

A350310 Alternating row sums of A066448.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A350737 Expansion of Sum_{k>=0} (-1)^k * x^(k*(3*k+1)/2) / Product_{j=1..k} (1-x^j).

Views

Author

Keywords

Crossrefs

Programs

PARI

A350737 Expansion of Sum_{k>=0} (-1)^k * x^(k(3k+1)/2) / Product_{j=1..k} (1-x^j).