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Search: id:A072964
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| A072964 |
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Number of partitions of n-th triangular number n(n+1)/2 (A000217(n)) into triangular parts. |
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4
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| 1, 1, 2, 4, 7, 15, 32, 66, 141, 295, 619, 1286, 2654, 5460, 11066, 22357, 44962, 89258, 176459, 347103, 675846, 1309903, 2525893, 4830943, 9196093, 17418788, 32772432, 61375543, 114401182, 212026732, 391231769, 718710706, 1313781686
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OFFSET
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0,3
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COMMENT
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What is limit_{n->inf} a(n)^(1/n)?
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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a(n) = A007294[n(n+1)/2] = coefficient of x^[n(n+1)/2] in the expansion of product_{k=1..inf} 1/(1 - x^(k(k+1)/2)).
a(n)=A007294(A000217(n)).
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MATHEMATICA
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c = CoefficientList[ Series[1/Product[1 - x^(i(i + 1)/2), {i, 1, 50}], {x, 0, 565}], x]; c[[Range[33]*(Range[33] + 1)/2 + 1]] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A007294, A073420, A114738.
Adjacent sequences: A072961 A072962 A072963 this_sequence A072965 A072966 A072967
Sequence in context: A049885 A129682 A129981 this_sequence A030033 A135131 A032363
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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), Aug 13 2002
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EXTENSIONS
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Entry revised by njas, Jan 28 2007
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