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!)
A350525 G.f. A(x) satisfies: [x^(2*n-2)] A(x)^(n*(n+1)/2) = 0 and [x^(2*n-1)] A(x)^(n*(n+1)/2) = 0 for n > 1, with a(0) = 1, a(2) = 6. 1
1, 6, -36, 360, -4320, 57024, -816480, 12737088, -216950400, 3985853184, -77049957888, 1524488905728, -30107409053184, 576921511037952, -9954313034508288, 94929987120648192, 5615966537573179392, -686220690340602003456, 57421269146260788903936 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

EXAMPLE

G.f.: A(x) = 1 + 6*x - 36*x^2 + 360*x^3 - 4320*x^4 + 57024*x^5 - 816480*x^6 + 12737088*x^7 - 216950400*x^8 + 3985853184*x^9 + ...

The table of coefficients of x^k in A(x)^(n*(n+1)/2), for k>=0, begins:

n=1: [1, 6, -36, 360, -4320, 57024, -816480, 12737088, -216950400, ...];

n=2: [1, 18, 0, 0, 0, 0, -54432, 2659392, -85660416, 2267481600, -...];

n=3: [1, 36, 324, 0, 0, 0, -108864, 3359232, -75582720, 1451188224, ...];

n=4: [1, 60, 1260, 10080, 15120, -36288, 0, 0, 5598720, -245099520, ...];

n=5: [1, 90, 3240, 58320, 524880, 1889568, -272160, -6298560, 0, 0, 0, 0, ...]; ...

in which both coefficients of x^(2*n-2) and x^(2*n-1) in A(x)^(n^2) equal zero for n > 1.

PROG

(PARI) {a(n) = my(A=[1, 6], P); for(i=1, n, A=concat(A, 0); P = (#A+1)\2;

A[#A] = -polcoeff( Ser(A)^(P*(P+1)/2)/(P*(P+1)/2), #A-1) ); H=A; A[n+1]}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A250117, A350524.

Sequence in context: A053335 A222925 A108733 * A229530 A265474 A277474

Adjacent sequences: A350522 A350523 A350524 * A350526 A350527 A350528

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jan 03 2022

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 January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)