A147766 - OEIS

%I #15 Aug 22 2018 02:32:32

%S 1,0,2,2,5,6,13,16,30,40,66,90,142,192,290,396,575,782,1112,1500,2092,

%T 2808,3848,5132,6945,9192,12298,16178,21422,28000,36763,47748,62205,

%U 80334,103910,133458,171538,219150,280039,356020,452469,572548,724047

%N Successive differences of A000990.

%C Original definition: A000012^(-1) * A000990, where A000012^(-1) = the pairwise difference operator and A000990 = (1, 1, 3, 5, 10, 16, 29, 45, ...).

%C Triangle A147767 is constructed from A147766 in every column.

%F a(n) = A000990(n) - A000990(n-1) and a(0)=1.

%F G.f.: exp(2*Sum_{k>=1} (sigma_1(k) - 1)*x^k/k). - _Ilya Gutkovskiy_, Aug 21 2018

%F a(n) ~ exp(2*Pi*sqrt(n/3)) * Pi^2 / (4 * 3^(7/4) * n^(9/4)). - _Vaclav Kotesovec_, Aug 21 2018

%e A000990 = (1, 1, 3, 5, 10, 16, ...). Pairwise differences = (1, 0, 2, 2, 5, ...).

%Y Cf. A000990, A147767.

%K nonn

%O 0,3

%A _Gary W. Adamson_, Nov 11 2008

%E Definition changed and more terms added by _Olivier Gérard_, Jul 25 2016