A063262 Eighth column (k=7) of sextinomial array A063260.

4, 27, 104, 305, 756, 1667, 3368, 6354, 11340, 19327, 31680, 50219, 77324, 116055, 170288, 244868, 345780, 480339, 657400, 887589, 1183556, 1560251, 2035224, 2628950, 3365180, 4271319, 5378832

Offset

0,1

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Formula

a(n) = A063260(n+2, 7 )= (n+1)*(n+2)*(n^5+32*n^4+413*n^3+2722*n^2+9432*n+10080)/7!.

G.f.: (4-5*x+5*x^3-4*x^4+x^5)/(1-x)^8; the numerator polynomial is N6(7, x) from row n=7 of array A063261.

a(n) = 4*C(n+2,2) + 15*C(n+2,3) + 20*C(n+2,4) + 15*C(n+2,5) + 6*C(n+2,6) + C(n+2,7) (see comment in A213888). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012

Mathematica

CoefficientList[Series[(4-5x+5x^3-4x^4+x^5)/(1-x)^8, {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {4, 27, 104, 305, 756, 1667, 3368, 6354}, 30] (* Harvey P. Dale, Mar 07 2023 *)

Crossrefs

Cf. A062989, A063260, A063261, A063263, A063264, A213888.

Sequence in context: A296316 A071175 A352331 * A156223 A048102 A171469

Adjacent sequences: A063259 A063260 A063261 * A063263 A063264 A063265

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 24 2001

Status

approved