login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307862 Coefficient of x^n in (1 + x - n*x^2)^n. 4
1, 1, -3, -17, 49, 651, -1259, -38023, 26433, 2969299, 2225101, -289389891, -692529551, 33718183045, 143578976997, -4559187616649, -29119975483135, 699788001188403, 6188699469443869, -119828491083854707, -1404529670244379599, 22563726025297759345, 341997845736800473397 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also coefficient of x^n in the expansion of 1/sqrt(1 - 2*x + (1+4*n)*x^2).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..floor(n/2)} (-n)^k * binomial(n,k) * binomial(n-k,k) = Sum_{k=0..floor(n/2)} (-n)^k * binomial(n,2*k) * binomial(2*k,k).

PROG

(PARI) {a(n) = polcoef((1+x-n*x^2)^n, n)}

(PARI) {a(n) = sum(k=0, n\2, (-n)^k*binomial(n, k)*binomial(n-k, k))}

(PARI) {a(n) = sum(k=0, n\2, (-n)^k*binomial(n, 2*k)*binomial(2*k, k))}

CROSSREFS

Main diagonal of A307860.

Cf. A002426, A187018, A307885.

Sequence in context: A144640 A084069 A297514 * A132124 A011917 A018691

Adjacent sequences:  A307859 A307860 A307861 * A307863 A307865 A307866

KEYWORD

sign

AUTHOR

Seiichi Manyama, May 02 2019

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)