OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
E.g.f. for offset 2: exp(sinh(x))*Product_{k>=1} cosh(x^(2*k)/(2*k)!). - Geoffrey Critzer, Jan 02 2011
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(irem(i, 2)=1 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(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] == 1 || Mod[j, 2] == 0, multinomial[n, Join[{n-i*j}, Table[i, {j}]]]/j!*b[n-i*j, i-1], 0], {j, 0, n/i}]]] ; a[n_] := b[n, n]; Table[ a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 16 2015, after Alois P. Heinz *)
PROG
(PARI) N=31; x='x+O('x^N);
Vec(serlaplace(exp(sinh(x))*prod(k=1, N, cosh(x^(2*k)/(2*k)!))))
/* gives: [1, 1, 1, 2, 8, 27, 82, 338, 1647, 7668, ...] , Joerg Arndt, Jan 03 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 10 2005, Aug 05 2007
EXTENSIONS
Offset changed to 0 and two 1's prepended by Alois P. Heinz, Mar 08 2015
STATUS
approved