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3, 30, 141, 513, 1815, 5727, 15882, 42417, 108165, 255831, 585258, 1302966, 2762349, 5705829, 11577633, 22708053, 43675938, 83011398, 153929484, 281210994, 509494515, 905832642, 1591395774, 2778237765, 4776943011
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OFFSET
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0,1
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COMMENTS
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where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and
A038500(n) is the highest power of 3 dividing n.
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LINKS
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EXAMPLE
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G.f.: T_1(q) = 3 + 30*q + 141*q^2 + 513*q^3 + 1815*q^4 + 5727*q^5 +...
Terms are divisible by 3:
A/3=[1,10,47,171,605,1909,5294,14139,36055,85277,195086,434322,...].
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PROG
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(PARI) {a(n)=local(L=sum(m=1, 3*n+1, 3*3^valuation(m, 3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n+1))); polcoeff(exp(L), 3*n+1)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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