A143278 Convolution of A006352 and A010815.

1, -25, -49, 0, 0, 121, 0, 169, 0, 0, 0, 0, -289, 0, 0, -361, 0, 0, 0, 0, 0, 0, 529, 0, 0, 0, 625, 0, 0, 0, 0, 0, 0, 0, 0, -841, 0, 0, 0, 0, -961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1225, 0, 0, 0, 0, 0, 1369, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1681, 0, 0, 0, 0, 0, 0, -1849, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,2

References

S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 188

Links

Table of n, a(n) for n=0..89.

Formula

Expansion of product of f(-q) * P(q) where f(), P() are Ramanujan series.

G.f.: Sum_{k} (-1)^k * (6*k - 1)^2 * x^(k * (3*k - 1) / 2).

G.f.: (Sum_{k} (-1)^k * x^(k * (3*k - 1) / 2)) * (1 - 24 * Sum_{k>0} k * x^k / (1 -x^k)).

Example

q - 25*q^25 - 49*q^49 + 121*q^121 + 169*q^169 - 289*q^289 - 361*q^361 + ...

Prog

(PARI) {a(n) = local(m); if(issquare(n = 24*n+1, &m), n * kronecker(12, m))}

Crossrefs

Sequence in context: A367496 A154082 A216869 * A106632 A284666 A090093

Adjacent sequences: A143275 A143276 A143277 * A143279 A143280 A143281

Keyword

sign

Author

Michael Somos, Aug 04 2008

Status

approved