A099753 a(n) = (2*n+1)^(n+2).

1, 27, 625, 16807, 531441, 19487171, 815730721, 38443359375, 2015993900449, 116490258898219, 7355827511386641, 504036361936467383, 37252902984619140625, 2954312706550833698643, 250246473680347348787521, 22550116774162743178682911, 2154025884392726618070214209

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..345

Formula

From Peter Bala, Aug 06 2012: (Start)

E.g.f.: d^2/dx^2{(2*x/T(2*x))^(3/2)*1/(1 - T(2*x))} = 1 + 27*x + 625*x^2/2! + ..., where T(x) is the tree function sum {n >=1} n^(n-1)*x^n/n! of A000169.

For r = 0, 1, 2, ..., the e.g.f. for the sequence (2*n+1)^(n+r) can be expressed in terms of the function U(z) = sum {n >= 0} (2*n+1)^(n-1)*z^(2*n+1)/(2^n*n!). See A214406 for details. In the present case, r = 2, and the resulting e.g.f. is 1/z*U(z)*(1 + 8*U(z)^2 + 3*U(z)^4)/(1 - U(z)^2)^5 taken at z = sqrt(2*x).

(End)

Maple

seq((2*n+1)^(n+2), n=0..30); # G. C. Greubel, Sep 03 2019

Mathematica

Table[(2*n+1)^(n+2), {n, 0, 30}] (* G. C. Greubel, Sep 03 2019 *)

Prog

(PARI) vector(30, n, (2*n-1)^(n+1)) \\ G. C. Greubel, Sep 03 2019
(Magma) [(2*n+1)^(n+2): n in [0..30]]; // G. C. Greubel, Sep 03 2019
(Sage) [(2*n+1)^(n+2) for n in (0..30)] # G. C. Greubel, Sep 03 2019
(GAP) List([0..30], n-> (2*n+1)^(n+2)); # G. C. Greubel, Sep 03 2019

Crossrefs

Cf. A000169, A085527, A085528, A214406.

Sequence in context: A185891 A185883 A212670 * A231292 A046359 A223500

Adjacent sequences: A099750 A099751 A099752 * A099754 A099755 A099756

Keyword

nonn,easy

Author

Kari Lajunen (Kari.Lajunen(AT)Welho.com), Nov 11 2004

Extensions

Terms a(13) onward added by G. C. Greubel, Sep 03 2019

Status

approved