A170752 Expansion of g.f.: (1+x)/(1-32*x).

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992, 1246704751477586336415744

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..664
• Index entries for linear recurrences with constant coefficients, signature (32).

Crossrefs

Cf. A003945.

Programs

GAP

k:=33;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

Magma

k:=33; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

Maple

k:=33; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

Mathematica

With[{k = 33}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

PARI

vector(26, n, k=33; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

Python

for i in range(1001):print(i,33*32**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=33; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*33^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 33*32^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (1/32)*(33*exp(32*x) - 1) - Stefano Spezia, Oct 09 2019