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

0,2

Links

Table of n, a(n) for n=0..18.

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

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*)

Prog

(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])

Crossrefs

Cf. A355408.

Sequence in context: A267657 A303057 A354263 * A113663 A082545 A074638

Adjacent sequences: A369792 A369793 A369794 * A369796 A369797 A369798

Keyword

nonn

Author

Prabha Sivaramannair, Feb 01 2024

Status

approved