OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..449
FORMULA
E.g.f.: 1 / (1 - Sum_{k>=0} x^(4*k+1) / (4*k+1)!).
E.g.f.: 1 / (1 - (sin(x) + sinh(x)) / 2).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 4 k + 1] a[n - 4 k - 1], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 23}]
nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(4 k + 1)/(4 k + 1)!, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+1)/(4*k+1)!)))) \\ Seiichi Manyama, Mar 23 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 16 2022
STATUS
approved