A056003 A second-order recursive sequence.

1, 18, 135, 660, 2475, 7722, 21021, 51480, 115830, 243100, 481338, 906984, 1637610, 2848860, 4796550, 7845024, 12503007, 19468350, 29683225, 44401500, 65270205, 94427190, 134617275, 189329400, 262957500, 360988056, 490217508, 659002960, 877549860, 1158240600

Offset

0,2

References

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = (n+1)*C(n+8, 8).

G.f.: (1+8*x)/(1-x)^10.

a(n) = A245334(n+8,8)/A000142(8). - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=0} 1/a(n) = 4*Pi^2/3 - 266681/22050.

Sum_{n>=0} (-1)^n/a(n) = 2*Pi^2/3 - 38656*log(2)/105 + 611409/2450. (End)

Maple

a:=n->(sum((numbcomp(n, 9)), j=9..n)):seq(a(n), n=9..35); # Zerinvary Lajos, Aug 26 2008

Mathematica

a[n_] := (n+1)*Binomial[n+8, 8]; Array[a, 50, 0] (* Amiram Eldar, Jan 15 2023 *)

Prog

(Haskell)
a056003 n = (n + 1) * a007318' (n + 8) 8
-- Reinhard Zumkeller, Aug 31 2014
(PARI) a(n) = (n+1)*binomial(n+8, 8) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Partial sums of A056117.

Cf. A093644 ((9, 1) Pascal, column m=9).

Cf. A000142, A007318, A052206, A245334, A254142 (partial sums).

Sequence in context: A320677 A010824 A022710 * A337002 A239208 A114239

Adjacent sequences: A056000 A056001 A056002 * A056004 A056005 A056006

Keyword

nonn,easy

Author

Barry E. Williams, Jun 12 2000

Status

approved