The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A336217 a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} binomial(n,k)^2 * a(k). 0
 1, 2, 18, 362, 12946, 723402, 58208490, 6375093258, 911949196434, 165104835435146, 36903191037412618, 9980525774650881738, 3212329170232153022314, 1213419234370490738427722, 531582989226188067128503722, 267336170027296964096123899962 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = (n!)^2 * [x^n] 1 / (1 - 2 * Sum_{k>=1} x^k / (k!)^2). a(n) = (n!)^2 * [x^n] 1 / (3 - 2 * BesselI(0,2*sqrt(x))). a(n) ~ (n!)^2 / (2 * BesselI(1, 2*sqrt(r)) * r^(n + 1/2)), where r = 0.4473998881770456142157108538567782213913712561... is the root of the equation 2*BesselI(0, 2*sqrt(r)) = 3. - Vaclav Kotesovec, Jul 17 2020 MATHEMATICA a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n, k]^2 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 15}] nmax = 15; CoefficientList[Series[1/(1 - 2 Sum[x^k/(k!)^2, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^2 CROSSREFS Cf. A004123, A102221. Sequence in context: A181536 A132911 A291902 * A226837 A152684 A201732 Adjacent sequences: A336214 A336215 A336216 * A336218 A336219 A336220 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 12 2020 STATUS approved

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

Last modified December 7 23:32 EST 2022. Contains 358671 sequences. (Running on oeis4.)