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A081040 5th binomial transform of (1,4,0,0,0,0,....). 5
1, 9, 65, 425, 2625, 15625, 90625, 515625, 2890625, 16015625, 87890625, 478515625, 2587890625, 13916015625, 74462890625, 396728515625, 2105712890625, 11138916015625, 58746337890625, 308990478515625, 1621246337890625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (10,-25).

FORMULA

a(n) = 10*a(n-1)-25*a(n-2), a(0)=1, a(1)=9.

a(n) = (4n+5)*5^(n-1).

a(n) = sum( k=0..n, (k+1)*4^k Binomial(n, k) ).

G.f.: (1-x)/(1-5x)^2.

MATHEMATICA

CoefficientList[Series[(1 - x) / (1 - 5 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

PROG

(MAGMA) [(4*n+5)*5^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

(PARI) a(n)=(4*n+5)*5^(n-1) \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A081039, A081041.

Sequence in context: A250415 A237040 A055284 * A102902 A127534 A037548

Adjacent sequences:  A081037 A081038 A081039 * A081041 A081042 A081043

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 03 2003

STATUS

approved

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Last modified January 19 22:02 EST 2018. Contains 297938 sequences.