OFFSET
0,1
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..500
G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128; see pp. 118 and 124.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.
Wikipedia, G. N. Watson.
Index entries for linear recurrences with constant coefficients, signature (50,-49).
FORMULA
From Colin Barker, Sep 27 2019: (Start)
G.f.: (5 - 7*x) / ((1 - x)*(1 - 49*x)).
a(n) = 50*a(n-1) - 49*a(n-2) for n>1.
(End)
EXAMPLE
For m=1 and n=0, p(7^(2*1+1)*0 + a(1)) = p(243) = 133978259344888 = 7^2 * 2734250190712.
For m=1 and n=1, p(7^(2*1+1)*1 + a(1)) = p(586) = 224282898599046831034631 = 7^2 * 4577202012225445531319.
PROG
(PARI) a(n) = (17 * 7^(2*n+1) + 1)/24; \\ Michel Marcus, Sep 25 2019
(PARI) Vec((5 - 7*x) / ((1 - x)*(1 - 49*x)) + O(x^15)) \\ Colin Barker, Sep 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Petros Hadjicostas, Sep 23 2019
STATUS
approved