A022654 Expansion of Product_{m>=1} (1+m*q^m)^26.

1, 26, 377, 4030, 35282, 267020, 1804855, 11133278, 63635364, 340845830, 1725623406, 8314033858, 38329313893, 169845329890, 726114272520, 3004404814658, 12063899757390, 47120073874016, 179388891204380, 666854279935844, 2424357631391397, 8631804737992852

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=26 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^26:m in [1..40]])[1..50] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Jul 18 2018

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(
      26*(-d)^(n/d+1), d=numtheory[divisors](n)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
       add(b(j)*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 18 2018

Mathematica

With[{nmax=50}, CoefficientList[Series[Product[(1+m*q^m)^26,{m,1,nmax}],{q,0,nmax}],q]] (* G. C. Greubel, Jul 18 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^26)) \\ G. C. Greubel, Jul 18 2018