OFFSET
0,2
COMMENTS
One of the congruences related to the partition numbers stated by Ramanujan.
REFERENCES
Berndt and Rankin, "Ramanujan: letters and commentaries", AMS-LMS, History of mathematics, vol. 9, pp. 192-193.
G. H. Hardy, Ramanujan, Cambridge Univ. Press, 1940. - From N. J. A. Sloane, Jun 07 2012
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
J. L. Drost, A Shorter Proof of the Ramanujan Congruence Modulo 5, Amer. Math. Monthly 104(10) (1997), 963-964.
Lasse Winquist, An elementary proof of p(11m+6) == 0 (mod 11), J. Combinatorial Theory 6(1) (1969), 56-59. MR0236136 (38 #4434). - From N. J. A. Sloane, Jun 07 2012
FORMULA
a(n) = (1/7)*A000041(7n+5).
MATHEMATICA
Table[PartitionsP[7n+5]/7, {n, 0, 24}] (* Jean-François Alcover, Nov 30 2015 *)
PROG
(PARI) a(n)=if(n<0, 0, n=7*n+5; polcoeff(1/eta(x+x*O(x^n)), n)/7)
(PARI) {a(n)=local(A, B); if(n<0, 0, A=x*O(x^n); B=eta(x^7+A); A=eta(x+A); polcoeff( B^3/A^4 +x*7*B^7/A^8, n))} /* Michael Somos, Jan 01 2006 */
(PARI) a(n) = numbpart(7*n+5)/7; \\ Michel Marcus, Nov 30 2015
(Magma) a:= func< n | NumberOfPartitions((7*n+5)) div 7 >; [ a(n) : n in [0..30]]; // Vincenzo Librandi, Nov 30 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jun 24 2002
STATUS
approved