login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A281708 a(n) = (Sum_{k=1..n} k^3 * p(k) * p(n-k)) * 2/n where p = A000041. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Cf. A000041, A067567.

Sequence in context: A303374 A037420 A034721 * A107815 A042803 A182876

Adjacent sequences:  A281705 A281706 A281707 * A281709 A281710 A281711

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 28 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 01:54 EST 2020. Contains 331328 sequences. (Running on oeis4.)