OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..243
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * A354520(2*k) * binomial(2*n-1,2*k-1) * a(n-k). - Seiichi Manyama, Aug 17 2022
MAPLE
a:= n-> coeff(series(cos(x)^cos(x), x, 2*n+1), x, 2*n)*(2*n)!:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 17 2023
MATHEMATICA
f[x_] := Cos[x]^Cos[x]; Table[Derivative[2*n][f][0], {n, 0, 30}]
PROG
(PARI) a354520(n) = sum(k=1, n\2, (16^k-4^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^j*a354520(2*j)*binomial(2*i-1, 2*j-1)*v[i-j+1])); v; \\ Seiichi Manyama, Aug 17 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Michel Lagneau, Aug 14 2012
STATUS
approved