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A162426 Row 3 of table A162424. 6
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; text; internal format)
OFFSET
0,2
LINKS
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).
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.
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))}
CROSSREFS
Sequence in context: A323580 A002799 A285263 * A374627 A058554 A342646
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2009
STATUS
approved

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Last modified July 23 04:10 EDT 2024. Contains 374544 sequences. (Running on oeis4.)