A064055 Ninth column of quadrinomial coefficients.

3, 31, 155, 546, 1554, 3823, 8451, 17205, 32802, 59268, 102388, 170261, 273975, 428418, 653242, 973998, 1423461, 2043165, 2885169, 4014076, 5509328, 7467801, 10006725, 13266955, 17416620, 22655178, 29217906

Offset

0,1

Links

Table of n, a(n) for n=0..26.

Formula

a(n)= A008287(n+3, 8)= binomial(n+3, 3)*(n^5+46*n^4+875*n^3+7118*n^2+23880*n+20160)/(8!/3!), n >= 0.

G.f.: (3+4*x-16*x^2+15*x^3-6*x^4+x^5 )/(1-x)^9, numerator polynomial is N4(8, x) from the array A063421.

a(n) = 3*C(n+3,3) + 19*C(n+3,4) + 30*C(n+3,5) + 21*C(n+3,6) + 7*C(n+3,7) + C(n+3,8) (see comment in A071675). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012

Mathematica

Table[3Binomial[n+3, 3]+19Binomial[n+3, 4]+30Binomial[n+3, 5]+21 Binomial[n+3, 6]+ 7 Binomial[n+3, 7]+ Binomial[n+3, 8], {n, 0, 30}] (* Harvey P. Dale, Apr 30 2022 *)

Crossrefs

A001919 (eighth column).

Sequence in context: A069615 A087389 A294394 * A227049 A078604 A195603

Adjacent sequences: A064052 A064053 A064054 * A064056 A064057 A064058

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 29 2001

Status

approved