|
|
A022572
|
|
Expansion of Product_{m>=1} (1+x^m)^7.
|
|
3
|
|
|
1, 7, 28, 91, 259, 665, 1589, 3585, 7707, 15925, 31808, 61677, 116536, 215180, 389194, 690935, 1206016, 2072700, 3511851, 5872545, 9701097, 15844866, 25606840, 40974528, 64956836, 102076289, 159084401, 245995792, 377574402, 575459136, 871189669, 1310492547, 1959326215, 2912370944
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ (7/3)^(1/4) * exp(Pi * sqrt(7*n/3)) / (32 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015
G.f.: exp(7*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018
|
|
MATHEMATICA
|
nmax=50; CoefficientList[Series[Product[(1+q^m)^7, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)
|
|
PROG
|
(PARI) x='x+O('x^51); Vec(prod(m=1, 50, (1 + x^m)^7)) \\ Indranil Ghosh, Apr 03 2017
(Magma) Coefficients(&*[(1+x^m)^7:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|