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A294221
Exponential transform of the square pyramidal numbers (A000330).
0
1, 1, 6, 30, 192, 1471, 12637, 120723, 1267492, 14438913, 176961001, 2318180239, 32275104644, 475285152707, 7373223596299, 120078748361611, 2046720320727328, 36414341169682417, 674650306604656821, 12988470845576660407, 259348785562811740236, 5361803880323803698731, 114593610390850499426211
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, Square Pyramidal Number
FORMULA
E.g.f.: exp(exp(x)*x*(6 + 9*x + 2*x^2)/6).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 6*x^2/2! + 30*x^3/3! + 192*x^4/4! + 1471*x^5/5! + 12637*x^6/6! + ...
MATHEMATICA
Range[0, 22]! CoefficientList[Series[Exp[Exp[x] x (6 + 9 x + 2 x^2)/6], {x, 0, 22}], x]
a[n_] := a[n] = Sum[a[n - k] Binomial[n - 1, k - 1] k (k + 1) (2 k + 1)/6, {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 25 2017
STATUS
approved