A372738 Binomial transform of A369795.

1, 4, 28, 298, 4240, 75394, 1608688, 40045618, 1139279680, 36463487554, 1296712045648, 50724943433938, 2164652356532320, 100072984472662114, 4982304066392196208, 265770533884409878258, 15122101633293034668160, 914210942121577873619074, 58519992421072004957876368, 3954059527570115477197922578

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{j=1..n} (1-(-1)^j-(-2)^j)*binomial(n,j)*a(n-j) for n > 0.

a(n) = 2^n + Sum_{j=1..n} (3^j-1)*binomial(n,j)*a(n-j).

a(n) = 1 + Sum_{j=1..n} (2^j-(-1)^j)*binomial(n,j)*a(n-j).

E.g.f.: exp(2*x)/(1 + exp(x) - exp(3*x)). - Vaclav Kotesovec, Jun 01 2024

Mathematica

nmax = 20; CoefficientList[Series[E^(2*x)/(1 + E^x - E^(3*x)), {x, 0, nmax}], x]*Range[0, nmax]! (* Vaclav Kotesovec, Jun 01 2024 *)

Prog

(SageMath)
def a(n):
    if n==0:
        return 1
    else:
        return sum([(1-(-1)^j-(-2)^j)*binomial(n, j)*a(n-j) for j in [1, .., n]])
list(a(n) for n in [0, .., 20])

Crossrefs

Cf. A369795, A355408.

Sequence in context: A343709 A354147 A362475 * A274043 A007152 A345248

Adjacent sequences: A372735 A372736 A372737 * A372739 A372740 A372741

Keyword

nonn

Author

Prabha Sivaramannair, May 11 2024

Status

approved