The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A207081 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1 + (1+x)^k). 2
 1, 2, 5, 14, 44, 151, 560, 2221, 9353, 41575, 194148, 948716, 4834965, 25624951, 140886544, 801808675, 4714489141, 28590416466, 178551890345, 1146748103103, 7564646759295, 51195535619574, 355096311786622, 2521828180324820, 18321335891780843, 136055733744848751 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..300 FORMULA G.f.: Sum_{n>=0, k=0..n*(n+1)/2} A053632(n,k)*x^n*(1+x)^k, where A053632(n,k) = number of partitions of k into distinct parts <= n. G.f.: 1/(G(0) - 2*x) where G(k) = 1 + x + x*(1 + x)^k - x*(1 + (1 + x)^(k+1))/G(k+1); (recursively defined continued fraction; G(0)=2*x). - Sergei N. Gladkovskii, Dec 15 2012 EXAMPLE G.f.: A(x) = 1 + 2*x + 5*x^2 + 14*x^3 + 44*x^4 + 151*x^5 + 560*x^6 +... such that, by definition, A(x) = 1 + x*(1 + (1+x)) + x^2*(1 + (1+x))*(1 + (1+x)^2) + x^3*(1 + (1+x))*(1 + (1+x)^2)*(1 + (1+x)^3) +... PROG (PARI) {a(n)=polcoeff(sum(m=0, n, x^m*prod(k=1, m, (1+(1+x)^k)+x*O(x^n))), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A053632. Sequence in context: A149884 A149885 A149886 * A148336 A257273 A119021 Adjacent sequences:  A207078 A207079 A207080 * A207082 A207083 A207084 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 19 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)