A006976 Coefficients of Chebyshev T polynomials: a(n) = A053120(n+12, n), n >= 0. (Formerly M4907)

1, 13, 98, 560, 2688, 11424, 44352, 160512, 549120, 1793792, 5637632, 17145856, 50692096, 146227200, 412778496, 1143078912, 3111714816, 8341487616, 22052208640, 57567870976, 148562247680, 379364311040, 959384125440

Offset

0,2

Comments

Binomial transform of A069039. - Paul Barry, Feb 19 2003

If X_1, X_2, ..., X_n are 2-blocks of a (2n+1)-set X then, for n >= 5, a(n-5) 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.: (1-x)/(1-2*x)^7.

a(n) = 2^n*binomial(n+5, 5)*(n+12)/12. [See a comment in A053120 on subdiagonal sequences. - Wolfdieter Lang, Jan 03 2020]

a(n) = Sum_{k = 0..floor((n+12)/2)} C(n+12,2*k)*C(k,6). - Paul Barry, May 15 2003

E.g.f.: (1/45)*exp(2*x)*(45 + 495*x + 1125*x^2 + 900*x^3 + 300*x^4 + 42*x^5 + 2*x^6). - Stefano Spezia, Jan 03 2020

Maple

seq(2^(n-1)*binomial(n+5, 5)*(n+12)/6, n=0..25); # G. C. Greubel, Aug 27 2019

Mathematica

Table[2^(n-1)*Binomial[n+5, 5]*(n+12)/6, {n, 0, 25}] (* G. C. Greubel, Aug 27 2019 *)
LinearRecurrence[{14, -84, 280, -560, 672, -448, 128}, {1, 13, 98, 560, 2688, 11424, 44352}, 30] (* Harvey P. Dale, Sep 26 2024 *)

Prog

(Magma) [2^(n-1)/6*Binomial(n+5, 5)*(n+12) : n in [0..25]]; // Brad Clardy, Mar 10 2012
(PARI) vector(26, n, 2^(n-2)*binomial(n+4, 5)*(n+11)/6) \\ G. C. Greubel, Aug 27 2019
(Sage) [2^(n-1)*binomial(n+5, 5)*(n+12)/6 for n in (0..25)] # G. C. Greubel, Aug 27 2019
(GAP) List([0..25], n-> 2^(n-1)*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: A372770 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