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Search: id:A162427
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| 1, 4, 10, 33, 68, 123, 226, 342, 547, 778, 1071, 1412, 1901, 2392, 2997, 3762, 4391, 5534, 6645, 7632, 9045, 10546, 11983, 13870, 16011, 17672, 20107, 22986, 25297, 28100, 31223, 34468, 38215, 42194, 45419, 50134, 54671, 59154, 64431, 70022
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^4 for n>=0 where S(x) = Sum_{n>=0} x^((n+1)(n+2)/2-1).
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EXAMPLE
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The coefficients in the 4-th power of the series:
S = 1 + x^2 + x^5 + x^9 + x^14 + x^20 + x^27 + x^35 + x^44 +...
begin: [(1),(0,4),(0,6,4),(4,12,1,16),(6,16,12,12,12),...];
the sums of the grouped coefficients yield the initial terms of this sequence.
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PROGRAM
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(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^4, m))}
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CROSSREFS
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Cf. A162424, A162425, A162426, A162428, A162429, A162433 (variant).
Sequence in context: A028283 A151746 A110145 this_sequence A165730 A052366 A052367
Adjacent sequences: A162424 A162425 A162426 this_sequence A162428 A162429 A162430
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 03 2009
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