This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A131490 #27 Jan 05 2025 19:51:38
%S A131490 1,1,3,16,130,1485,22645,444136,10889676,326345460,11736144420,
%T A131490 498798542880,24732729791484,1415034219327729,92523874454996985,
%U A131490 6856434802243346320,571604206230905727880,53259509403796625217288,5513868420471764306104008
%N A131490 Appears in Taylor series of powers of generalized Bessel functions.
%C A131490 Integer sequence given between equations (16) and (17) of Bender et al., p. 4. A recursion is found for coefficients of Taylor series of r-th powers of generalized Bessel functions.
%C A131490 A001263^(-1) * [1, 2, 3, ...] = A103364 * [1, 2, 3, ...] = (1, 1, -1, 3, -16, 130, -1485, 22645, ...); where A001263 = the Narayana triangle. - _Gary W. Adamson_, Jan 02 2008
%C A131490 Image of n^2 under A001263^(-1), i.e., A001263^(-1) *[0,1,4,9,...] is [0, 1, 1, -3, 16, -130, 1485, -22645, 444136, ...]. - _Paul Barry_, Jul 13 2009
%H A131490 Carl M. Bender, Dorje C. Brody, and Bernhard K. Meister, <a href="http://dx.doi.org/10.1063/1.1526940">On powers of Bessel functions</a>, J. Math. Phys. vol 44, No. 1 (2003) pp 309-314.
%H A131490 Yan Hong, Bai-Ni Guo, and Feng Qi, <a href="https://doi.org/10.32604/cmes.2021.016431">Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind</a>, Computer Modeling in Engineering and Sciences (2021) Vol. 129, No. 1, 409-423.
%H A131490 F. T. Howard, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/23-3/howard.pdf">Integers Related to the Bessel Function J1(z)</a>, Fibonacci Quarterly, Volume 23, Number 3, August 1985, pp. 249-257.
%F A131490 For n>1, a(n) = (Sum_{r=1..n-1} binomial(n+1,r+1)*binomial(n+1,r)*a(r)*a(n-r))/(n+1)^2. - _Michel Marcus_, Oct 17 2012
%p A131490 A131490 := proc(n) local twos,resul; resul := twos*taylor(BesselI(0,twos),twos=0,2*n+3) ; resul := resul/taylor(BesselI(1,twos),twos=0,2*n+3) ; resul := taylor(resul-4,twos=0,2*n+3) ; resul := coeftayl(resul,twos=0,2*n) ; resul := resul*4^n/2 ; abs(resul*factorial(n+1)*factorial(n)) ; end: seq(A131490(n),n=1..23) ; # _R. J. Mathar_, Jul 31 2007
%Y A131490 Cf. A001263, A103364.
%K A131490 nonn
%O A131490 1,3
%A A131490 _Jonathan Vos Post_, Jul 28 2007
%E A131490 More terms from _R. J. Mathar_, Jul 31 2007