OFFSET
0,2
COMMENTS
Binomial transform of A069038. - Paul Barry, Feb 19 2003
If X_1, X_2, ..., X_n are 2-blocks of a (2n+1)-set X then, for n>=4, a(n-4) is the number of (n+5)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 18 2007
The 5th corrector line for transforming 2^n offset 0 with a leading 1 into the Fibonacci sequence. - Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Milan Janjic, Two Enumerative Functions
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64).
FORMULA
G.f.: (1-x)/(1-2*x)^6. a(n) = 2^(n-1)*binomial(n+4, 4)*(n+10)/5, for n >= 0. [a(n) from Mar 06 2000 rewritten. See the Brad Clardy formula below, and a comment in A053120 on subdiagonals. - Wolfdieter Lang, Jan 03 2020]
a(n) = 2^(n-4)*(n+1)(n+2)(n+3)(n+4)(n+10)/15. - Paul Barry, Feb 19 2003
a(n) = Sum_{k=0..floor((n+10)/2)} C(n+10, 2k)*C(k, 5). - Paul Barry, May 15 2003
a(n) = -A039991(n+10, 10). - N. J. A. Sloane, May 16 2003
a(n) = binomial transform of b(n)= (2*n^5 + 10*n^4 + 30*n^3 + 50*n^2 + 43*n + 15) / 15 offset 0. a(3) = 364. - Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009
a(n) = 2^(n-1)/5*binomial(n+4,4)*(n+10). - Brad Clardy, Mar 10 2012
E.g.f.: (1/15)*exp(2*x)*(15+135*x+240*x^2+140*x^3+30*x^4+2*x^5). - Stefano Spezia, Jan 03 2020
MATHEMATICA
Table[2^(n-1)/5*Binomial[n+4, 4]*(n+10), {n, 0, 30}] (* Paolo Xausa, Jun 26 2024 *)
PROG
(Magma) [2^(n-1)/5*Binomial(n+4, 4)*(n+10): n in [0..25]]; // Brad Clardy, Mar 10 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name clarified by Wolfdieter Lang, Nov 26 2019
STATUS
approved