A174432 Partial sums of A000699.

1, 2, 6, 33, 281, 3111, 41343, 635202, 11036914, 213638812, 4555901812, 106107724162, 2679887230354, 72962091956750, 2130453028323070, 66421485491085025, 2202438789394598209, 77400308039913410963

Offset: 1

Author

Jonathan Vos Post, Mar 19 2010

Keywords

• easy
• nonn

Comments

Partial sums of number of irreducible diagrams (in the sense of perturbation expansion in quantum field theory: spinor case in 4 spacetime dimensions) with 2n nodes. The subsequence of primes in this partial sum begins: 2, 281, and there never seem to be any more, as the underlying sequence is all even after A000699(8).

Examples

			a(18) = 1 + 1 + 4 + 27 + 248 + 2830 + 38232 + 593859 + 10401712 + 202601898 + 4342263000 + 101551822350 + 2573779506192 + 70282204726396 + 2057490936366320 + 64291032462761955 + 2136017303903513184 + 75197869250518812754.
		

Crossrefs

Cf. A000699, A004300, A051862.

Formula

a(n) = SUM[i=1..n] A000699(i), where those A000699(n) = (n-1)*SUM[i=1..n-1] A000699(i)*A000699(n-i).