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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054440 Number of ordered pairs of partitions of n with no common parts. 13
 1, 0, 2, 4, 12, 16, 48, 60, 148, 220, 438, 618, 1302, 1740, 3216, 4788, 8170, 11512, 19862, 27570, 45448, 64600, 100808, 141724, 223080, 307512, 465736, 652518, 968180, 1334030, 1972164, 2691132, 3902432, 5347176, 7611484, 10358426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..5000 Sylvie Corteel, Carla D. Savage, Herbert S. Wilf, Doron Zeilberger, A pentagonal number sieve, J. Combin. Theory Ser. A 82 (1998), no. 2, 186-192. Eric Weisstein's World of Mathematics, Pentagonal Number Theorem Wikipedia, Pentagonal number theorem FORMULA G.f.: Sum[p(n)^2*x^n]/Sum[p(n)*x^n], with p(n)=number of partitions of n. a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n)) / (64 * 2^(1/4) * n^(7/4)). - Vaclav Kotesovec, May 20 2018 EXAMPLE a(3)=4 because of the 4 pairs of partitions of 3: (3,21),(3,111),(21,3),(111,3). MAPLE with(combinat): p1 := sum(numbpart(n)^2*x^n, n=0..500): it := p1*product((1-x^i), i=1..500): s := series(it, x, 500): for i from 0 to 100 do printf(`%d, `, coeff(s, x, i)) od: MATHEMATICA nmax = 50; CoefficientList[Series[Sum[PartitionsP[k]^2*x^k, {k, 0, nmax}]/Sum[PartitionsP[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 04 2016 *) PROG (Haskell) a054440 = sum . zipWith (*) a087960_list . map a001255 . a260672_row -- Reinhard Zumkeller, Nov 15 2015 CROSSREFS Cf. A000041, A001255, A001318, A087960, A260672, A260664, A260669, A304873, A304877. Main diagonal of A284592. Sequence in context: A132314 A053636 A181135 * A308076 A303819 A074646 Adjacent sequences:  A054437 A054438 A054439 * A054441 A054442 A054443 KEYWORD easy,nonn AUTHOR Herbert S. Wilf, May 13 2000 EXTENSIONS Corrected and extended by James A. Sellers, May 23 2000 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.

Last modified April 13 21:24 EDT 2021. Contains 342941 sequences. (Running on oeis4.)