A213261 - OEIS

%I #35 Sep 27 2019 02:46:10

%S 7,77,490,2436,10143,37338,124754,386155,1121505,3087735,8118264,

%T 20506255,49995925,118114304,271248950,607163746,1327710076,

%U 2841940500,5964539504,12292341831,24908858009,49686288421,97662728555,189334822579,362326859895,684957390936,1280011042268,2366022741845,4328363658647,7840656226137

%N a(n) = p(7*n + 5), where p(k) = number of partitions of k = A000041(k).

%C It is known that a(n) is divisible by 7 (see A071746).

%H Seiichi Manyama, <a href="/A213261/b213261.txt">Table of n, a(n) for n = 0..1000</a>

%H Ho-Hon Leung, <a href="https://arxiv.org/abs/1802.08443">Another Identity for Complete Bell Polynomials based on Ramanujan's Congruences</a>, arXiv:1802.08443 [math.CO], 2018.

%H Ho-Hon Leung, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Leung/leung4.html">Another Identity for Complete Bell Polynomials based on Ramanujan's Congruences</a>, J. Integer Seq. 21 (2018), Article 18.6.4.

%H Lasse Winquist, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80105-5">An elementary proof of p(11m+6) == 0 (mod 11)</a>, J. Combinatorial Theory 6(1) (1969), 56-59. MR0236136 (38 #4434). - From _N. J. A. Sloane_, Jun 07 2012

%F a(n) = A000041(A017041(n)). - _Omar E. Pol_, Jan 18 2013

%F a(n) = 7 * A071746(n). - _Joerg Arndt_, Nov 06 2016

%t Table[PartitionsP[7 n + 5], {n, 0, 29}] (* _Jean-François Alcover_, Nov 12 2018 *)

%o (PARI) a(n) = numbpart(7*n+5); \\ _Michel Marcus_, Jan 07 2015

%Y Cf. A000041, A017041, A071734, A071746, A076394, A213256, A213260, A213261, A327582, A327714, A327770.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Jun 07 2012