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 A007465 Exponential-convolution 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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: A174319 A131458 A032205 * A261389 A073389 A320744 Adjacent sequences:  A007462 A007463 A007464 * A007466 A007467 A007468 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 6 19:22 EST 2019. Contains 329809 sequences. (Running on oeis4.)