A276041 Exponential convolution of odd numbers (A005408) with themselves.

1, 6, 28, 104, 336, 992, 2752, 7296, 18688, 46592, 113664, 272384, 643072, 1499136, 3457024, 7897088, 17891328, 40239104, 89915392, 199753728, 441450496, 970981376, 2126512128, 4638900224, 10083106816, 21843935232, 47177531392, 101602820096, 218238025728

Offset: 0

Author

Ilya Gutkovskiy, Aug 17 2016

Keywords

• nonn
• easy

Links

• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72. Erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8)

Crossrefs

Cf. A000079, A002061, A005408, A053755, A128796 (exponential convolution of even numbers with themselves).

Programs

Mathematica

LinearRecurrence[{6, -12, 8}, {1, 6, 28}, 29]
Table[2^n (n^2 + n + 1), {n, 0, 28}]

Formula

O.g.f.: (1 + 4*x^2)/(1 - 2*x)^3.

E.g.f.: (1 + 2*x)^2*exp(2*x).

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3).

a(n) = 2^n*(n^2 + n + 1).

a(n) = A000079(n)*A002061(n+1).

Binomial transform of A053755.