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A071746 a(n) = p(7n+5)/7 where p(k) denotes the k-th partition number. 12
1, 11, 70, 348, 1449, 5334, 17822, 55165, 160215, 441105, 1159752, 2929465, 7142275, 16873472, 38749850, 86737678, 189672868, 405991500, 852077072, 1756048833, 3558408287, 7098041203, 13951818365, 27047831797, 51760979985 (list; graph; refs; listen; history; text; internal format)
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).

a(n) = A000041(A017041(n))/7 = A213261(n)/7. - Omar E. Pol, Jan 18 2013

MATHEMATICA

Table[PartitionsP[7n+5]/7, {n, 0, 24}] (* Jean-Fran├žois 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

Cf. A000041, A017041, A071734, A076394, A213261, A327582, A327714, A327770.

Sequence in context: A211050 A295074 A173200 * A205812 A162568 A255205

Adjacent sequences:  A071743 A071744 A071745 * A071747 A071748 A071749

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 24 2002

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)