A007465 Exponential-convolution of triangular numbers with themselves.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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]

Crossrefs

Cf. A000217.

Programs

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 *)

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