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1, 3, 6, 13, 24, 34, 49, 69, 94, 117, 148, 174, 211, 249, 298, 331, 366, 439, 498, 535, 591, 670, 733, 792, 880, 939, 1006, 1123, 1212, 1270, 1353, 1456, 1599, 1648, 1750, 1896, 1963, 2127, 2164, 2379, 2452, 2545, 2709, 2848, 2997, 3094, 3276, 3385, 3595
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^3 for n>=0 where S(x) = Sum_{n>=0} x^((n+1)(n+2)/2-1).
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EXAMPLE
| The coefficients in the cube of the series:
S = 1 + x^2 + x^5 + x^9 + x^14 + x^20 + x^27 + x^35 + x^44 +...
begin: [(1),(0,3),(0,3,3),(1,6,0,6),(3,6,3,3,9),(1,12,0,6,9,6),...];
the sums of the grouped coefficients yield the initial terms of this sequence.
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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^3, m))}
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CROSSREFS
| Cf. A162424, A162425, A162427, A162428, A162429; A162432 (variant).
Sequence in context: A174369 A022811 A002799 * A058554 A128517 A022568
Adjacent sequences: A162423 A162424 A162425 * A162427 A162428 A162429
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 03 2009
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