A147766 Successive differences of A000990.

1, 0, 2, 2, 5, 6, 13, 16, 30, 40, 66, 90, 142, 192, 290, 396, 575, 782, 1112, 1500, 2092, 2808, 3848, 5132, 6945, 9192, 12298, 16178, 21422, 28000, 36763, 47748, 62205, 80334, 103910, 133458, 171538, 219150, 280039, 356020, 452469, 572548, 724047

Offset: 0

Author

Gary W. Adamson, Nov 11 2008

Keywords

• nonn

Comments

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

Triangle A147767 is constructed from A147766 in every column.

Examples

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

Crossrefs

Cf. A000990, A147767.

Formula

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

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

a(n) ~ exp(2*Pi*sqrt(n/3)) * Pi^2 / (4 * 3^(7/4) * n^(9/4)). - Vaclav Kotesovec, Aug 21 2018

Extensions

Definition changed and more terms added by Olivier Gérard, Jul 25 2016