A281708 a(n) = (Sum_{k=1..n} k^3 * p(k) * p(n-k)) * 2/n where p = A000041.

2, 17, 66, 218, 564, 1407, 3074, 6536, 12960, 24991, 46028, 83166, 145182, 249151, 417432, 688742, 1114978, 1782228, 2804886, 4365560, 6709074, 10208894, 15368870, 22937184, 33916388, 49763175, 72429396, 104685554, 150234266, 214249998, 303606838, 427780502

Offset: 1

Author

Michael Somos, Jan 28 2017

Keywords

• nonn

Comments

See A067567 for a conjecture about this sequence from Peter Bala.

Examples

			G.f. = 2*x + 17*x^2 + 66*x^3 + 218*x^4 + 564*x^5 + 1407*x^6 + 3074*x^7 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000041, A067567.

Programs

Mathematica

a[n_]:= (2/n)*Sum[k^3*PartitionsP[k]*PartitionsP[n-k], {k,1,n}]; Table[a[n], {n,1,50}] (* G. C. Greubel, Jul 29 2018 *)

PARI

{a(n) = if( n<1, 0, sum(k=1, n, k^3 * numbpart(k) * numbpart(n-k)) * 2 / n)};