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A162425 Row 2 of table A162424. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)