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A279361
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Exponential transform of the triangular numbers.
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10
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1, 1, 4, 16, 80, 471, 3127, 23059, 186468, 1635265, 15422471, 155388399, 1663294756, 18826525771, 224434810797, 2808247979611, 36770685485408, 502505495269521, 7150461569849395, 105723461155720879, 1621191824611307436, 25738508587975433251
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OFFSET
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0,3
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LINKS
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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]
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FORMULA
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E.g.f.: exp(exp(x)*x*(x+2)/2).
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EXAMPLE
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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! + ...
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MAPLE
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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:
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MATHEMATICA
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Range[0, 23]! CoefficientList[Series[Exp[Exp[x] x (x + 2)/2], {x, 0, 23}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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