A144516 a(n) = (15*n^2+45*n-70)*binomial(n+4,6)/8.

0, 0, 10, 175, 1225, 5565, 19425, 56595, 144375, 332475, 705705, 1401400, 2632630, 4718350, 8121750, 13498170, 21754050, 34118490, 52229100, 78233925, 114911335, 165809875, 235410175, 329311125, 454442625, 619307325, 834253875, 1111784310

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: 5x^2(2+17x+2x^2)/(1-x)^9. - R. J. Mathar, Jan 17 2009

a(n) = (3*n^8 + 36*n^7 + 142*n^6 + 144*n^5 - 293*n^4 - 516*n^3 + 148*n^2 + 336*n)/1152. - Charles R Greathouse IV, Jun 03 2026

Maple

f:=n->(15*n^2+45*n-70)*binomial(n+4, 6)/8;

Mathematica

Table[((15n^2+45n-70)Binomial[n+4, 6])/8, {n, 0, 30}] (* Harvey P. Dale, Dec 12 2018 *)

Prog

(PARI) a(n)=(3*n^8+36*n^7+142*n^6+144*n^5-293*n^4-516*n^3+148*n^2+336*n)/1152 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

A diagonal of A144385.

Sequence in context: A078516 A304445 A268936 * A053537 A049380 A302105

Adjacent sequences: A144513 A144514 A144515 * A144517 A144518 A144519

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Dec 17 2008

Status

approved