OFFSET
1,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
H. E. Salzer, Tables of coefficients for obtaining central differences from the derivatives, Journal of Mathematics and Physics (this journal is also called Studies in Applied Mathematics), 42 (1963), 162-165, plus several inserted tables.
H. E. Salzer, Annotated scanned copy of left side of Table III
FORMULA
From Peter Bala, Oct 03 2019: (Start)
a(n) are the denominators in the expansion of (1/2)*(d/dx)(2*sinh(sqrt(x)/2))^4 =
x + (1/4)*x^2 + (1/40)*x^3 + (17/12096)*x^4 + (31/604800)*x^5 + ...
The a(n) also appear as denominators in the difference formula: (1/2)*f(x+2) - f(x+1) + f(x-1) - (1/2)*f(x-2) = D^3(f(x)) + (1/4)*D^5(f(x)) + (1/40)*D^7(f(x)) + (17/12096)*D^9(f(x)) + ..., where D denotes the differential operator d/dx.
(End)
MAPLE
gf := (sinh(2*sqrt(x)) - 2*sinh(sqrt(x)))/sqrt(x): ser := series(gf, x, 20):
seq(denom(coeff(ser, x, n)), n=1..14); # Peter Luschny, Oct 05 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Dec 20 2016
STATUS
approved
