A294221 Exponential transform of the square pyramidal numbers (A000330).

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

Table of n, a(n) for n=0..22.

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

Index to sequences related to pyramidal numbers

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

Cf. A000330, A033462, A279361, A281231.

Sequence in context: A109501 A239488 A147517 * A005922 A278008 A370751

Adjacent sequences: A294218 A294219 A294220 * A294222 A294223 A294224

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 25 2017

Status

approved