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A276041 Exponential convolution of odd numbers (A005408) with themselves. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..28.

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)

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.

MATHEMATICA

LinearRecurrence[{6, -12, 8}, {1, 6, 28}, 29]

Table[2^n (n^2 + n + 1), {n, 0, 28}]

CROSSREFS

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

Sequence in context: A172141 A172132 A011856 * A134416 A266976 A117999

Adjacent sequences:  A276038 A276039 A276040 * A276042 A276043 A276044

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Aug 17 2016

STATUS

approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)