A022579 Expansion of Product_{m>=1} (1+x^m)^14.
1, 14, 105, 574, 2576, 10052, 35273, 113794, 342699, 974176, 2635955, 6833540, 17061345, 41197422, 96544003, 220212384, 490104727, 1066552228, 2273590095, 4755188704, 9771319068, 19751596934, 39317784863, 77150246040, 149357609184, 285497384004, 539227765104, 1006978117880
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
Programs
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Magma
Coefficients(&*[(1+x^m)^14:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 25 2018
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Mathematica
nmax=50; CoefficientList[Series[Product[(1+q^m)^14,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *) -
PARI
m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^14)) \\ G. C. Greubel, Feb 25 2018
Formula
a(n) ~ (7/6)^(1/4) * exp(Pi * sqrt(14*n/3)) / (256 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015
a(0) = 1, a(n) = (14/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017
G.f. A(x) = (1/2)*( G(sqrt(x)) + G(-sqrt(x)) )/G(x^4), where G(x) = Product_{n >= 1} 1/(1 - x^n)^4 is the g.f. of A023003 (see also A000727). - Peter Bala, Oct 05 2023