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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A187540 Binomial partial sums of the central Lah numbers. 11
 1, 3, 41, 1315, 63825, 4116611, 331127353, 31915763811, 3585520583585, 460054836028675, 66377105303195721, 10637410917472061603, 1874707445757653437681, 360356280811211873453955, 75028021167256736753934425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA Formula: a(n) = 1+sum(binomial(n,k)binomial(2k-1,k-1)(2k)!/k!,k=0..n). Recurrence: for n>=3, a(n) = 1/n*(-2 +(32 - 48*n + 16*n^2)*a(n-3) + (-31 + 63*n - 32*n^2)*a(n-2) + (3 - 14*n + 16*n^2)*a(n-1) ) E.g.f.: exp(x) (1/2 + 1/Pi K(16x) ), where K(z) is the elliptic integral of the first kind (defined as in Mathematica). a(n) ~ 16^n*n^(n-1/2)*exp(1/16-n)/sqrt(2*Pi). - Vaclav Kotesovec, Aug 09 2013 MAPLE seq(1+add(binomial(n, k)*binomial(2*k-1, k-1)*(2*k)!/k!, k=1..n), n=0..20); MATHEMATICA Table[1 + Sum[Binomial[n, k]Binomial[2k-1, k-1](2k)!/k!, {k, 1, n}], {n, 0, 20}] PROG (Maxima) makelist(1+sum(binomial(n, k)*binomial(2*k-1, k-1)*(2*k)!/k!, k, 1, n), n, 0, 12); (PARI) a(n) = 1+sum(k=0, n, binomial(n, k)*binomial(2*k-1, k-1)*(2*k)!/k!) \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Cf. A187536, A008297, A111596, A187538, A187539, A187542, A187543, A187544, A187545, A187546, A187547, A187548. Sequence in context: A012035 A012016 A207993 * A012104 A012147 A012011 Adjacent sequences: A187537 A187538 A187539 * A187541 A187542 A187543 KEYWORD nonn,easy,nice AUTHOR Emanuele Munarini, Mar 11 2011 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 June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)