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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335310 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * (-n)^(n-k). 3
1, 1, -2, 11, -74, 477, -804, -84425, 3315334, -102211207, 3005297956, -88338323709, 2627003399164, -78764141488043, 2341929797646648, -66394419743289105, 1609460569459689286, -18001777147777896975, -1625299659961386724524, 196005371138608184827003 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = central coefficient of (1 - (n - 2)*x - (n - 1)*x^2)^n.
a(n) = [x^n] 1 / sqrt(1 + 2*(n - 2)*x + n^2*x^2).
a(n) = n! * [x^n] exp((2 - n)*x) * BesselI(0,2*sqrt(1 - n)*x).
a(n) = Sum_{k=0..n} binomial(n,k)^2 * (1-n)^k.
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n, k] Binomial[n + k, k] (-n)^(n - k), {k, 0, n}], {n, 1, 19}]]
Table[SeriesCoefficient[1/Sqrt[1 + 2 (n - 2) x + n^2 x^2], {x, 0, n}], {n, 0, 19}]
Table[n! SeriesCoefficient[Exp[(2 - n) x] BesselI[0, 2 Sqrt[1 - n] x], {x, 0, n}], {n, 0, 19}]
Table[Hypergeometric2F1[-n, -n, 1, 1 - n], {n, 0, 19}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)^2*(1-n)^k); \\ Michel Marcus, Jun 01 2020
CROSSREFS
Sequence in context: A049671 A074609 A299786 * A199417 A114179 A231556
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 31 2020
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 December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)