

A006976


Coefficients of Chebyshev T polynomials: a(n) = A053120(n+12, n), n >= 0.
(Formerly M4907)


12



1, 13, 98, 560, 2688, 11424, 44352, 160512, 549120, 1793792, 5637632, 17145856, 50692096, 146227200, 412778496, 1143078912, 3111714816, 8341487616, 22052208640, 57567870976, 148562247680, 379364311040, 959384125440
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Binomial transform of A069039.  Paul Barry, Feb 19 2003
If X_1, X_2, ..., X_n are 2blocks of a (2n+1)set X then, for n >= 5, a(n5) is the number of (n+6)subsets of X intersecting each X_i, (i = 1, 2, ..., n).  Milan Janjic, Nov 18 2007


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

G. C. Greubel, Table of n, a(n) for n = 0..1000
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].
Milan Janjic, Two Enumerative Functions
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (14,84,280,560,672,448,128).


FORMULA

G.f.: (1x)/(12*x)^7.
a(n) = 2^n*binomial(n+5,5) * (n+12)/12.
a(n) = 2^n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+12)/1440.
a(n) = Sum_{k = 0..floor((n+12)/2)} C(n+12,2*k)*C(k,6).  Paul Barry, May 15 2003


MAPLE

seq(2^(n1)*binomial(n+5, 5)*(n+12)/6, n=0..25); # G. C. Greubel, Aug 27 2019


MATHEMATICA

Table[2^(n1)*Binomial[n+5, 5]*(n+12)/6, {n, 0, 25}] (* G. C. Greubel, Aug 27 2019 *)


PROG

(MAGMA) [2^(n1)/6*Binomial(n+5, 5)*(n+12) : n in [0..25]]; // Brad Clardy, Mar 10 2012
(PARI) vector(26, n, 2^(n2)*binomial(n+4, 5)*(n+11)/6) \\ G. C. Greubel, Aug 27 2019
(Sage) [2^(n1)*binomial(n+5, 5)*(n+12)/6 for n in (0..25)] # G. C. Greubel, Aug 27 2019
(GAP) List([0..25], n> 2^(n1)*Binomial(n+5, 5)*(n+12)/6); # G. C. Greubel, Aug 27 2019


CROSSREFS

a(n) = A039991(n+12, 12), A053120.
Partial sums are in A002409.
Sequence in context: A228680 A158795 A075899 * A282992 A295271 A034270
Adjacent sequences: A006973 A006974 A006975 * A006977 A006978 A006979


KEYWORD

nonn,easy


AUTHOR

Simon Plouffe


EXTENSIONS

More terms from James A. Sellers, Aug 21 2000
Name clarified by Wolfdieter Lang, Nov 26 2019


STATUS

approved



