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Search: id:A129519
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| A129519 |
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First differences of the binomial transform of the distinct partition numbers (A000009). |
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1
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| 1, 1, 2, 5, 12, 28, 65, 151, 350, 807, 1850, 4221, 9597, 21760, 49215, 111032, 249856, 560835, 1255854, 2805969, 6256784, 13925698, 30941050, 68634679, 152009239, 336152787, 742276931, 1636747349, 3604206106, 7926412320, 17410413153
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = Product_{n>=1} [1 + x^n/(1-x)^n].
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EXAMPLE
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Product formula is illustrated by:
A(x) = [1 + x + x^2 + x^3 + x^4 + x^5 +...]*
[1 + x^2 + 2x^3 + 3x^4 + 4x^5 + 5x^6 +...]*
[1 + x^3 + 3x^4 + 6x^5 + 10x^6 + 15x^7 +...]*
[1 + x^4 + 4x^5 + 10x^6 + 20x^7 + 35x^8 +...]*
[1 + x^5 + 5x^6 + 15x^7 + 35x^8 + 70x^9 +...]*...*
[1 + Sum_{k>=n+1} C(k-1,n)*x^k ]*...
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PROGRAM
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(PARI) {a(n)=polcoeff(prod(k=0, n, 1+sum(i=k+1, n, binomial(i-1, k)*x^i +x*O(x^n))), n)}
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CROSSREFS
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Cf. A000009.
Sequence in context: A019486 A019485 A018914 this_sequence A034943 A166297 A024960
Adjacent sequences: A129516 A129517 A129518 this_sequence A129520 A129521 A129522
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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 18 2007
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