login
A279361
Exponential transform of the triangular numbers.
10
1, 1, 4, 16, 80, 471, 3127, 23059, 186468, 1635265, 15422471, 155388399, 1663294756, 18826525771, 224434810797, 2808247979611, 36770685485408, 502505495269521, 7150461569849395, 105723461155720879, 1621191824611307436, 25738508587975433251
OFFSET
0,3
LINKS
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]
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Exponential Transform
Eric Weisstein's World of Mathematics, Triangular Number
FORMULA
E.g.f.: exp(exp(x)*x*(x+2)/2).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 16*x^3/3! + 80*x^4/4! + 471*x^5/5! + 3127*x^6/6! + ...
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1)*j*(j+1)/2*a(n-j), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Dec 11 2016
MATHEMATICA
Range[0, 23]! CoefficientList[Series[Exp[Exp[x] x (x + 2)/2], {x, 0, 23}], x]
CROSSREFS
Sequence in context: A171454 A316944 A020080 * A374982 A003471 A002777
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 10 2016
STATUS
approved