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A081908 2^n*(n^2-n+8)/8. 4
1, 2, 5, 14, 40, 112, 304, 800, 2048, 5120, 12544, 30208, 71680, 167936, 389120, 892928, 2031616, 4587520, 10289152, 22937600, 50855936, 112197632, 246415360, 538968064, 1174405120, 2550136832, 5519704064, 11911823360, 25635586048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A000124 (when this begins 1,1,2,4,7,...). 2nd binomial transform of (1,0,1,0,0,0,.....). Case k=2 where a(n,k)=k^n(n^2-n+2k^2)/(2k^2) with G.f. (1-2kx+(k^2+1)x^2)/(1-kx)^3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

FORMULA

G.f.: (1-4x+5x^2)/(1-2x)^3

a(n)=A000079(n)+(A001788(n)-A001787(n))/2. - Paul Barry, May 27 2003

sum{k=0..n, C(n, k)(1+C(k, 2)) } - Paul Barry, May 27 2003

PROG

(MAGMA) [2^n*(n^2-n+8)/8: n in [0..40]]; Vincenzo Librandi, Apr 27 2011

(PARI) a(n)=2^n*(n^2-n+8)/8 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A081909.

Sequence in context: A126219 A111110 A111109 * A221677 A229737 A059505

Adjacent sequences:  A081905 A081906 A081907 * A081909 A081910 A081911

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 31 2003

STATUS

approved

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Last modified October 18 10:28 EDT 2017. Contains 293507 sequences.