

A007465


Exponentialconvolution of triangular numbers with themselves.
(Formerly M4195)


1



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, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]


FORMULA

G.f.: (16*x^4+12*x^310*x^2+4*x)/(2*x1)^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}] (* JeanFrançois Alcover, Feb 24 2019 *)


CROSSREFS

Cf. A000217.
Sequence in context: A174319 A131458 A032205 * A261389 A073389 A320744
Adjacent sequences: A007462 A007463 A007464 * A007466 A007467 A007468


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


STATUS

approved



