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Search: id:A163826
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| A163826 |
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G.f.: Sum_{n>=1} n*2^(n^2) * x^n/(1 - 2^n*x)^(n+1). |
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+0
1
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| 2, 40, 1944, 314432, 189747360, 445551600000, 4129013201798016, 151656774720556632064, 22103008531040898656506368, 12788356812264101562500000000000
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n) = n*2^n*(2^n + 1)^(n-1).
More generally, we have the identity:
Sum_{n>=1} n*q^(n^2)*x^n/(1-q^n*xy)^(n+1) = Sum_{n>=1} n*q^n*(q^n+y)^(n-1)*x^n.
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EXAMPLE
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G.f.: 2*x + 40*x^2 + 1944*x^3 + 314432*x^4 + 189747360*x^5 +...
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PROGRAM
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(PARI) a(n)=n*2^n*(2^n+1)^(n-1)
(PARI) {a(n)=polcoeff(sum(m=1, n, m*2^(m^2)*x^m/(1-2^m*x+O(x^(n-m)))^(m+1), n)}
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CROSSREFS
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Sequence in context: A012834 A012241 A099707 this_sequence A000816 A000819 A060079
Adjacent sequences: A163823 A163824 A163825 this_sequence A163827 A163828 A163829
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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 04 2009
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