A162425 Row 2 of table A162424.

1, 2, 3, 4, 7, 7, 8, 11, 13, 13, 16, 15, 19, 22, 21, 23, 22, 29, 27, 31, 30, 29, 39, 34, 37, 37, 40, 47, 41, 45, 46, 47, 53, 48, 55, 57, 53, 58, 57, 65, 62, 61, 65, 68, 71, 71, 69, 74, 75, 77, 74, 79, 87, 85, 82, 81, 91, 90, 93, 89, 93, 96, 95, 101, 100, 103, 101, 104, 107, 109

Offset

0,2

Links

Table of n, a(n) for n=0..69.

Formula

a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^2 for n>=0 where S(x) = Sum_{n>=0} x^((n+1)(n+2)/2-1).

Example

The coefficients in the square of the series:
S = 1 + x^2 + x^5 + x^9 + x^14 + x^20 + x^27 + x^35 + x^44 +...
begin: [(1),(0,2),(0,1,2),(0,2,0,2),(1,2,0,0,4),(0,2,0,1,2,2),...];
the sums of the grouped coefficients yield the initial terms of this sequence.

Prog

(PARI) {a(n)=local(S=sum(m=0, n+1, x^((m+1)*(m+2)/2-1))+O(x^((n+1)*(n+2)/2))); sum(m=n*(n+1)/2, n*(n+1)/2+n, polcoeff(S^2, m))}

Crossrefs

Cf. A162424, A162426, A162427, A162428, A162429, A162431 (variant).

Sequence in context: A265352 A265368 A239972 * A217254 A223488 A175686

Adjacent sequences: A162422 A162423 A162424 * A162426 A162427 A162428

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2009

Status

approved