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!)
A349584 G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x)^4 * A(x)^6. 4
1, 3, 14, 107, 1106, 13173, 168820, 2264298, 31356818, 444803666, 6429510234, 94356870748, 1402149248128, 21055387206719, 319007902203196, 4870481885025752, 74858763620576738, 1157339247553310574, 17985974981514604660, 280813589679135551721 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Second binomial transform of A002295.
LINKS
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(6*k,k) * 2^(n-k) / (5*k+1).
a(n) = 2^n*F([1/6, 1/3, 1/2, 2/3, 5/6, -n], [2/5, 3/5, 4/5, 1, 6/5], -3^6*(2/5)^5), where F is the generalized hypergeometric function. - Stefano Spezia, Nov 22 2021
a(n) ~ 2^(n - 15/2) * 26453^(n + 3/2) / (6561 * sqrt(3*Pi) * n^(3/2) * 5^(5*n + 3/2)). - Vaclav Kotesovec, Nov 26 2021
MATHEMATICA
nmax = 19; A[_] = 0; Do[A[x_] = 1/(1 - 2 x) + x (1 - 2 x)^4 A[x]^6 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Sum[Binomial[n, k] Binomial[6 k, k] 2^(n - k)/(5 k + 1), {k, 0, n}], {n, 0, 19}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(6*k, k)*2^(n-k)/(5*k+1)); \\ Michel Marcus, Nov 23 2021
CROSSREFS
Sequence in context: A167017 A051106 A246731 * A258298 A121951 A276751
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 22 2021
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 February 26 10:12 EST 2024. Contains 370343 sequences. (Running on oeis4.)