A006974 Coefficients of Chebyshev T polynomials: a(n) = A053120(n+8, n), n >= 0. (Formerly M4631)

1, 9, 50, 220, 840, 2912, 9408, 28800, 84480, 239360, 658944, 1770496, 4659200, 12042240, 30638080, 76873728, 190513152, 466944000, 1133117440, 2724986880, 6499598336, 15386804224, 36175872000, 84515225600, 196293427200, 453437816832

Offset

0,2

Comments

If X_1,X_2,...,X_n are 2-blocks of a (2n+1)-set X then, for n>=3, a(n-3) is the number of (n+4)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 18 2007

The fourth 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..25.

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

M. H. Albert, M. D. Atkinson, R. Brignall, The enumeration of three pattern classes using monotone grid classes, El. J. Combinat. 19 (3) (2012) P20, Chapter 5.4.1.

Index entries for sequences related to Chebyshev polynomials.

Formula

G.f.: (1-x)/(1-2*x)^5.

a(n) = Sum_{k=0..floor((n+8)/2)} C(n+8, 2k)*C(k, 4). - Paul Barry, May 15 2003

Binomial transform of a(n)=(24*n^4-134*n^3+261*n^2-130*n+3)/3 offset 0. a(3)=220. [Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009]

a(n) = 2^(n-3)*binomial(n+3, 3)*(n+8). - Brad Clardy, Mar 08 2012 [See a comment in A053120 on subdiagonals. - Wolfdieter Lang, Jan 03 2020]

E.g.f.: (1/3)*exp(2*x)*(3 + 21*x + 27*x^2 + 10*x^3 + x^4). - Stefano Spezia, Aug 17 2019

Maple

a := n->n*(n+1)*(n+2)*(n+7)*2^(n-5)/3;

Prog

(Magma) [2^(n-1)/4*Binomial(n+3, 3)*(n+8) : n in [0..25]]; // Brad Clardy, Mar 08 2012

Crossrefs

Cf. A039991 (see column 8), A003472 (partial sums), A053120.

Sequence in context: A116169 A280549 A084367 * A279979 A222993 A171480

Adjacent sequences: A006971 A006972 A006973 * A006975 A006976 A006977

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

Name clarified by Wolfdieter Lang, Nov 26 2019

Status

approved