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Search: id:A106337
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| A106337 |
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Number of ways of writing n as the sum of n triangular numbers. |
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+0
2
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| 0, 1, 1, 4, 13, 31, 82, 253, 757, 2173, 6341, 18888, 56266, 167324, 499773, 1499059, 4503557, 13546893, 40824379, 123233868, 372472353, 1127080252, 3414310032, 10353722919, 31425764410, 95463814056, 290222666436, 882954212908
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Log.g.f.: Sum_{n>=1} a(n)/n*x^n = log(G106336(x)), where G106336(x) is the g.f. of A106336 and satisfies: Sum_{n>=0} (x*G106336(x))^(n*(n+1)/2) = G106336(x).
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EXAMPLE
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G106336(x) = exp(x + 1/2*x^2 + 4/3*x^3 + 13/4*x^4 + 31/5*x^5 +...).
G106336(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 11*x^5 +...+ A106336(n)*x^n +...
G106336(x) = 1 + x*G106336(x) + (x*G106336(x))^3 + (x*G106336(x))^6 +...
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PROGRAM
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(PARI) {a(n)=local(X); if(n<1, 0, X=x+x*O(x^n); polcoeff(eta(X^2)^(2*n)/eta(X)^n, n))}
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CROSSREFS
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Cf. A106333, A106334, A106335, A106336.
Sequence in context: A011937 A097122 A116411 this_sequence A027998 A026567 A036487
Adjacent sequences: A106334 A106335 A106336 this_sequence A106338 A106339 A106340
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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), Apr 29 2005
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