The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A190738 Central coefficients of the Riordan matrix A104259. 1
1, 4, 27, 212, 1785, 15630, 140287, 1280592, 11833389, 110360150, 1036670272, 9794291556, 92972640761, 886023463122, 8471878678545, 81236546627920, 780898417097733, 7522708492892214, 72607180401922894, 701969331508141900, 6796919869909393140 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = T(2*n,n), where T(n,k) = A104259(n,k).
a(n) = sum(k=0..n, binomial(2*n,n+k)*binomial(n+2*k,k)*(n+1)/(n+k+1)).
Recurrence: 2*(n-1)*n*(2*n + 1)*(107*n^3 - 345*n^2 + 253*n + 12)*a(n) = (n-1)*(5029*n^5 - 16215*n^4 + 8284*n^3 + 13359*n^2 - 11675*n + 1974)*a(n-1) - 4*(2*n - 3)*(1498*n^5 - 4830*n^4 + 2899*n^3 + 3165*n^2 - 3254*n + 630)*a(n-2) + 100*(n-1)*(2*n - 5)*(2*n - 3)*(107*n^3 - 24*n^2 - 116*n + 27)*a(n-3). - Vaclav Kotesovec, Jul 05 2021
a(n) ~ sqrt(c) * d^n / sqrt(Pi*n), where d = 9.945658804810730213397409025621... is the real root of the equation -400 + 112*d - 47*d^2 + 4*d^3 = 0 and c = 0.3447849735035503206155951176700724872157... is the real root of the equation -125 - 173*c + 963*c^2 + 1712*c^3 = 0. - Vaclav Kotesovec, Jun 05 2022
MATHEMATICA
Table[Sum[Binomial[2n, n+k]Binomial[n+2k, k](n+1)/(n+k+1), {k, 0, n}], {n, 0, 20}]
PROG
(Maxima) makelist(sum(binomial(2*n, n+k)*binomial(n+2*k, k)*(n+1)/(n+k+1), k, 0, n), n, 0, 20);
CROSSREFS
Cf. A104259.
Sequence in context: A026005 A059391 A371786 * A361717 A275607 A319518
KEYWORD
nonn
AUTHOR
Emanuele Munarini, May 18 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 16:46 EDT 2024. Contains 373432 sequences. (Running on oeis4.)