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!)
A319939 O.g.f. A(x) satisfies: [x^n] exp(-n^2*A(x)) / (1 - n*x)^n = 0, for n > 0. 7
1, 1, 3, 24, 325, 6642, 176204, 5828160, 228372291, 10374419250, 534203188948, 30762752950224, 1956914341159778, 136286437739608492, 10310240639621093400, 841935232438747348480, 73807352585103519962815, 6913603998931859925828282, 689148541231545351838902508, 72838943589708142133363904400, 8137053663063956034586144506558, 958035702236154579666369909892724 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
It is remarkable that this sequence should consist entirely of integers.
LINKS
FORMULA
a(n) ~ c * d^n * n! / n^3, where d = 6.1103392... and c = 0.05165... - Vaclav Kotesovec, Oct 24 2020
EXAMPLE
O.g.f.: A(x) = x + x^2 + 3*x^3 + 24*x^4 + 325*x^5 + 6642*x^6 + 176204*x^7 + 5828160*x^8 + 228372291*x^9 + 10374419250*x^10 + ...
ILLUSTRATION OF DEFINITION.
The table of coefficients of x^k/k! in exp(-n^2*A(x)) / (1 - n*x)^n begins:
n=1: [1, 0, -1, -16, -567, -38816, -4771025, -886931424, ...];
n=2: [1, 0, 0, -40, -2112, -154464, -19097600, -3549131520, ...];
n=3: [1, 0, 9, 0, -3483, -333504, -43269795, -8050921776, ...];
n=4: [1, 0, 32, 224, 0, -454016, -75031040, -14515172352, ...];
n=5: [1, 0, 75, 800, 21225, 0, -92559125, -22271154000, ...];
n=6: [1, 0, 144, 1944, 88128, 2515104, 0, -25624491264, ...];
n=7: [1, 0, 245, 3920, 252693, 10516576, 505622425, 0, ...];
n=8: [1, 0, 384, 7040, 602112, 30829056, 2210682880, 134210187264, 0, ...];
in which the coefficient of x^n in row n forms a diagonal of zeros.
RELATED SERIES.
exp(A(x)) = 1 + x + 3*x^2 + 25*x^3/3! + 673*x^4/4! + 42501*x^5/5! + 5048251*x^6/6! + 924544573*x^7/7! + 242568147585*x^8/8! + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); m=#A; A[m] = Vec( exp(-m^2*x*Ser(A))/(1-m*x +x^2*O(x^m))^m)[m+1]/m^2 ); A[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A264561 A003236 A232693 * A082166 A354259 A370055
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2018
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 May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)