A006975 Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+10, n), n >= 0. (Formerly M4796)

1, 11, 72, 364, 1568, 6048, 21504, 71808, 228096, 695552, 2050048, 5870592, 16400384, 44843008, 120324096, 317521920, 825556992, 2118057984, 5369233408, 13463453696, 33426505728, 82239815680, 200655503360, 485826232320

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

Table of n, a(n) for n=0..23.

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 sequences related to Chebyshev polynomials.

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

Prog

(Magma) [2^(n-1)/5*Binomial(n+4, 4)*(n+10): n in [0..25]]; // Brad Clardy, Mar 10 2012

Crossrefs

First differences of A054849.

Cf. A039991, A053120, A069038.

Sequence in context: A092044 A156149 A258402 * A260585 A084900 A300968

Adjacent sequences: A006972 A006973 A006974 * A006976 A006977 A006978

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

Name clarified by Wolfdieter Lang, Nov 26 2019

Status

approved