OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
FORMULA
E.g.f.: exp(cosh(x)-1)*Product_{k>0} cosh(x^(2*k-1)/(2*k-1)!).
MAPLE
A:= proc(n) exp(cosh(x)-1) *mul(cosh(x^(2*k-1)/ (2*k-1)!), k=1..n) end: a:= n-> coeff(series(A(n), x, 2*n+1), x, 2*n) *(2*n)!: seq(a(n), n=0..20); # Alois P. Heinz, Sep 29 2008
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
`if`(irem(i, 2)=0 or j=0 or irem(j, 2)=0, multinomial(
n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
end:
a:= n-> b(2*n$2):
seq(a(n), n=0..30); # Alois P. Heinz, Mar 08 2015
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[If[Mod[i, 2]==0 || j==0 || Mod[j, 2]==0, multinomial[n, {n - i j} ~Join~ Table[i, {j}]]/j! b[n - i j, i-1], 0], {j, 0, n/i}]]];
a[n_] := b[2n, 2n];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 19 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 05 2007, Aug 05 2007
EXTENSIONS
More terms from Alois P. Heinz, Sep 29 2008
STATUS
approved