A034858 a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15.

7, 38, 93, 180, 308, 487, 728, 1043, 1445, 1948, 2567, 3318, 4218, 5285, 6538, 7997, 9683, 11618, 13825, 16328, 19152, 22323, 25868, 29815, 34193, 39032, 44363, 50218, 56630, 63633, 71262, 79553

Offset

2,1

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: x^2*(-7-3*x+27*x^2-25*x^3+7*x^4)/(x-1)^5 . - R. J. Mathar, Apr 03 2017

Mathematica

Table[Binomial[n+3, 4]+3Binomial[n+1, 3]+5Binomial[n-1, 2]+7n-15, {n, 2, 40}] (* Harvey P. Dale, Feb 04 2016 *)

Prog

(PARI) x='x+O('x^30); Vec(x^2*(7+3*x-27*x^2+25*x^3-7*x^4)/(1-x)^5) \\ G. C. Greubel, Feb 22 2018
(Magma) [Binomial(n+3, 4)+3*Binomial(n+1, 3)+5*Binomial(n-1, 2)+7*n-15: n in [2..40]]; // G. C. Greubel, Feb 22 2018

Crossrefs

Sequence in context: A346278 A165495 A369355 * A249354 A249021 A114290

Adjacent sequences: A034855 A034856 A034857 * A034859 A034860 A034861

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved