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A162427
Row 4 of table A162424.
6
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
OFFSET
0,2
FORMULA
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).
EXAMPLE
The coefficients in the 4th 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.
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^4, m))}
CROSSREFS
Sequence in context: A185631 A174520 A179654 * A165730 A052366 A309682
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2009
STATUS
approved