This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307722 G.f. A(x) satisfies: A(x) = x*exp(2*Sum_{n>=1} Sum_{k>=1} n*a(n)*x^(n*(2*k-1))/(2*k - 1)). 0
 0, 1, 2, 10, 78, 794, 9870, 143610, 2382350, 44266538, 909575170, 20468012850, 500542618118, 13218631046786, 374965272837542, 11372416113131346, 367296622702990270, 12587154399475110546, 456238999451039779510, 17440439387336903608866, 701272672299320517560470 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} ((1 + x^n)/(1 - x^n))^(n*a(n)). EXAMPLE G.f.: A(x) = x + 2*x^2 + 10*x^3 + 78*x^4 + 794*x^5 + 9870*x^6 + 143610*x^7 + 2382350*x^8 + 44266538*x^9 + ... MATHEMATICA a[n_] := a[n] = SeriesCoefficient[x Exp[2 Sum[Sum[j a[j] x^(j (2 k - 1))/(2 k - 1), {k, 1, n - 1}], {j, 1, n - 1}]], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 20}] a[n_] := a[n] = SeriesCoefficient[x Product[((1 + x^k)/(1 - x^k))^(k a[k]), {k, 1, n - 1}], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 20}] CROSSREFS Cf. A073075, A307708, A307709. Sequence in context: A212381 A098692 A300994 * A138273 A301388 A052568 Adjacent sequences:  A307719 A307720 A307721 * A307723 A307724 A307725 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 24 2019 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 July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)