This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A106261 Expansion of 1/sqrt(1 - 20*x - 20*x^2). 5
 1, 10, 160, 2800, 51400, 970000, 18640000, 362800000, 7128700000, 141103000000, 2809273600000, 56197096000000, 1128614356000000, 22741607080000000, 459548117440000000, 9309106936000000000, 188980474087000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Central coefficient of (1 + 10x + 30x^2)^n. Tenth binomial transform of 1/sqrt(1 - 120x^2). In general, 1/sqrt(1 - 4*r*x - 4*r*x^2) has e.g.f. exp(2rx)*BesselI(0,2r*sqrt((r+1)/r)x)), and a(n) = Sum_{k=0..n} C(2k,k)*C(k,n-k)*r^k gives the central coefficient of (1 + (2r)*x + r(r+1)*x^2) and is the (2r)-th binomial transform of 1/sqrt(1 - 8*C(n+1,2)x^2). LINKS G. C. Greubel, Table of n, a(n) for n = 0..750 Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5. FORMULA E.g.f.: exp(10*x)*BesselI(0, 10*sqrt(6/5)*x). a(n) = Sum_{k=0..n} C(2k, k)*C(k, n-k)*5^k. n*a(n) + 10*(-2*n+1)*a(n-1) + 20*(-n+1)*a(n-2) = 0. - R. J. Mathar, Nov 26 2012 a(n) ~ sqrt((1+sqrt(5/6))/2) * (10+2*sqrt(30))^n / sqrt(Pi*n). - Vaclav Kotesovec, Oct 19 2013 MATHEMATICA CoefficientList[Series[1/Sqrt[1-20*x-20*x^2], {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2013 *) PROG (PARI) for(n=0, 25, print1(sum(k=0, n, binomial(2*k, k)*binomial(k, n-k)*5^k), ", ")) \\ G. C. Greubel, Jan 31 2017 CROSSREFS Cf. A006139, A106258, A106259, A106260. Sequence in context: A116041 A284110 A180881 * A112125 A090374 A034724 Adjacent sequences:  A106258 A106259 A106260 * A106262 A106263 A106264 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 28 2005 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 December 5 20:54 EST 2019. Contains 329779 sequences. (Running on oeis4.)