A369795 Binomial transform of A355408.

1, 3, 21, 225, 3201, 56913, 1214361, 30229545, 860016801, 27525472353, 978858962601, 38291126920665, 1634047719138801, 75542860973042193, 3761030066169432441, 200624240375801784585, 11415336789685550907201, 690117422445926970890433, 44175435307592982599575881

Offset: 0

Author

Prabha Sivaramannair, Feb 01 2024

Keywords

• nonn

Crossrefs

Cf. A355408.

Programs

Mathematica

nmax = 20; CoefficientList[Series[E^x/(1 + E^x - E^(3*x)), {x, 0, nmax}], x]*
Range[0, nmax]! (* Vaclav Kotesovec, Feb 01 2024*)

SageMath

def a(m):
    if m==0:
        return 1
    else:
        return 1+sum([(3^j-1)*binomial(m,j)*a(m-j) for j in [1,..,m]])
list(a(m) for m in [1,..,50])

Formula

a(n) = 1 + Sum_{k=1..n} (3^k - 1) * binomial(n,k) * a(n-k) for n > 0.

E.g.f.: exp(x)/(1 + exp(x) - exp(3*x)). - Vaclav Kotesovec, Feb 01 2024