

A109700


Number of partitions of n into parts each equal to 4 mod 5.


0



1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 3, 4, 2, 2, 3, 5, 4, 3, 3, 6, 6, 6, 4, 6, 7, 9, 7, 7, 8, 11, 11, 11, 9, 12, 14, 16, 13, 14, 16, 21, 20, 19, 18, 24, 26, 27, 24, 27, 31, 36, 34, 34, 35, 43, 45, 47, 43, 49, 55, 62, 58, 59, 63, 75, 77, 77, 75, 87
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OFFSET

0,19


LINKS

Table of n, a(n) for n=0..84.


FORMULA

G.f.: 1/product(1x^(4+5j), j=0..infinity).  Emeric Deutsch, Mar 30 2006
a(n) ~ GAMMA(4/5) * exp(Pi*sqrt(2*n/15)) / (2^(19/10) * 3^(2/5) * 5^(1/10) * Pi^(1/5) * n^(9/10)).  Vaclav Kotesovec, Feb 27 2015


EXAMPLE

a(30)=2 since 30 = 14+4+4+4+4 = 9+9+4+4+4


MAPLE

g:=1/product(1x^(4+5*j), j=0..25): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..90); # Emeric Deutsch, Mar 30 2006


MATHEMATICA

nmax=100; CoefficientList[Series[Product[1/(1x^(5*k+4)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)


CROSSREFS

Sequence in context: A069010 A256122 A087048 * A087742 A072530 A184341
Adjacent sequences: A109697 A109698 A109699 * A109701 A109702 A109703


KEYWORD

nonn


AUTHOR

Erich Friedman, Aug 07 2005


EXTENSIONS

More terms from Michael Somos, Aug 10 2005


STATUS

approved



