A281454 Exponential transform of the 4-dimensional figurate numbers (A002417).
1, 1, 9, 55, 441, 4316, 46867, 566714, 7550601, 109118728, 1696640501, 28209128344, 498557098921, 9320449092072, 183575505529431, 3796015849264216, 82156098504947473, 1856012774517648896, 43663382492497648777, 1067393396478808265656, 27062739020373087036281, 710410408414549934445376, 19277762831507022675509139
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + x/1! + 9*x^2/2! + 55*x^3/3! + 441*x^4/4! + 4316*x^5/5! + 46867*x^6/6! + ...
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
Programs
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Mathematica
Range[0, 22]! CoefficientList[Series[Exp[Exp[x] x (6 + 18 x + 9 x^2 + x^3)/6], {x, 0, 22}], x]
Formula
E.g.f.: exp(exp(x)*x*(6 + 18*x + 9*x^2 + x^3)/6).