This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003162 A binomial coefficient summation. (Formerly M2597) 2
 1, 1, 1, 3, 6, 19, 49, 163, 472, 1626, 5034, 17769, 57474, 206487, 688881, 2508195, 8563020, 31504240, 109492960, 406214878, 1432030036, 5349255726, 19077934506, 71672186953, 258095737156, 974311431094, 3537275250214, 13408623649893 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS H. W. Gould, Problem E2384, Amer. Math. Monthly, 81 (1974), 170-171. FORMULA G.f.: hypergeometric expression with an antiderivative, see Maple program. - Mark van Hoeij, May 06 2013 Recurrence: 4*n*(n+1)^2*(196*n^3 - 819*n^2 + 530*n + 528)*a(n) = 2*n*(1372*n^4 - 3633*n^3 - 7455*n^2 + 21934*n - 8448)*a(n-1) + (12740*n^6 - 90867*n^5 + 195310*n^4 - 13277*n^3 - 452690*n^2 + 528384*n - 174960)*a(n-2) + 8*(n-2)*(686*n^4 - 3010*n^3 + 1176*n^2 + 6543*n - 4725)*a(n-3) - 16*(n-3)^2*(n-2)*(196*n^3 - 231*n^2 - 520*n + 435)*a(n-4). - Vaclav Kotesovec, Mar 06 2014 a(n) ~ 4^(n+2)/(9*Pi*n^2). - Vaclav Kotesovec, Mar 06 2014 MAPLE H := hypergeom([1/2, 1/2], [1], 16*x^2); ogf := (Int(6*H*(4*x^2+5)/(4-x^2)^(3/2), x)+H*(16*x^2-1)/(4-x^2)^(1/2))*((2-x)/(2+x))^(1/2)/(4*x)+1/(8*x); series(ogf, x=0, 20);  # Mark van Hoeij, May 06 2013 MATHEMATICA Table[Sum[(Binomial[n, k]-Binomial[n, k-1])^3/Binomial[n, Floor[n/2]], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 06 2014 *) PROG (PARI) a(n)=if(n<0, 0, sum(k=0, n\2, (binomial(n, k)-binomial(n, k-1))^3)/binomial(n, n\2)) /* Michael Somos, Jun 02 2005 */ CROSSREFS Cf. A003161. Sequence in context: A148566 A148567 A148568 * A179277 A129417 A132335 Adjacent sequences:  A003159 A003160 A003161 * A003163 A003164 A003165 KEYWORD nonn AUTHOR 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 21:49 EDT 2018. Contains 316404 sequences. (Running on oeis4.)