A007465 - OEIS

A007465

Exponential-convolution of triangular numbers with themselves.
(Formerly M4195)

1, 6, 30, 128, 486, 1692, 5512, 17040, 50496, 144512, 401664, 1089024, 2890240, 7529472, 19298304, 48754688, 121602048, 299827200, 731643904, 1768685568, 4239261696, 10081796096, 23805296640, 55839817728, 130187001856, 301813727232, 696036360192, 1597358735360

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OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..27.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; 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]

FORMULA

G.f.: (-1-6*x^4+12*x^3-10*x^2+4*x)/(2*x-1)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]

E.g.f.: (1/4)*exp(2*x)*(2 + 4*x + x^2)^2. - Ilya Gutkovskiy, Mar 21 2018

MATHEMATICA

a = DifferenceRoot[Function[{a, n}, {(-2n^4 - 28n^3 - 158n^2 - 388n - 384)* a[n] + (n^4 + 10n^3 + 43n^2 + 74n + 64)*a[n+1] == 0, a[0] == 1}]];

Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Feb 24 2019 *)

CROSSREFS

Cf. A000217.

Sequence in context: A334326 A131458 A032205 * A261389 A073389 A320744

Adjacent sequences: A007462 A007463 A007464 * A007466 A007467 A007468

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved