%I A059618
%S A059618 1,1,1,3,4,6,10,15,21,30,43,59,82,111,148,199,263,344,451,584,751,965,
%T A059618 1230,1560,1973,2483,3110,3885,4834,5990,7405,9123,11202,13724,16762,
%U A059618 20417,24815,30081,36377,43900,52860,63511,76166,91157,108886,129842
%N A059618 Number of strongly unimodal partitions of n (strongly unimodal means 
               strictly increasing then strictly decreasing).
%F A059618 a(n) =A059619(n, 0) =sum_k[A059619(n, k)] for k>0 when n>0.
%F A059618 G.f.: 1+Sum_{k>=0} (x^(k+1)*Product_{i=1..k} (1+x^i)^2). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Dec 05 2003
%e A059618 a(6)=10 since 6 can be written as 6, 5+1, 4+2, 3+2+1, 2+4, 2+3+1, 1+5, 
               1+4+1, 1+3+2 or 1+2+3 (but for example neither 2+2+1+1 nor 1+2+2+1 
               which are only weakly unimodal).
%Y A059618 Cf. A000009, A000041, A001523, A059607, A059619.
%Y A059618 Sequence in context: A167410 A085378 A125869 this_sequence A114736 A099417 
               A139463
%Y A059618 Adjacent sequences: A059615 A059616 A059617 this_sequence A059619 A059620 
               A059621
%K A059618 nice,nonn
%O A059618 0,4
%A A059618 Henry Bottomley (se16(AT)btinternet.com), Jan 31 2001