A051880 a(n) = binomial(n+4,4)*(2*n+1).

1, 15, 75, 245, 630, 1386, 2730, 4950, 8415, 13585, 21021, 31395, 45500, 64260, 88740, 120156, 159885, 209475, 270655, 345345, 435666, 543950, 672750, 824850, 1003275, 1211301, 1452465, 1730575, 2049720, 2414280, 2828936, 3298680, 3828825, 4425015, 5093235

Offset

0,2

Comments

Old name was: Partial sums of A051799.

References

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

Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.

Links

Kelvin Voskuijl, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = C(n+4, 4)*(2n+1).

G.f.: (1+9*x)/(1-x)^6.

From Amiram Eldar, Sep 04 2025: (Start)

Sum_{n>=0} 1/a(n) = 128*log(2)/35 - 152/105.

Sum_{n>=0} (-1)^n/a(n) = 32*Pi/35 + 596/105 - 384*log(2)/35. (End)

Mathematica

Nest[Accumulate[#]&, Table[n(n+1)(10n-7)/6, {n, 0, 50}], 2] (* Harvey P. Dale, Nov 13 2013 *)

Crossrefs

Cf. A051799.

Cf. A093645 ((10, 1) Pascal, column m=5).

A diagonal of A280880.

Sequence in context: A211812 A266395 A260550 * A007328 A222909 A049391

Adjacent sequences: A051877 A051878 A051879 * A051881 A051882 A051883

Keyword

easy,nonn

Author

Barry E. Williams, Dec 14 1999

Extensions

Name changed by Alois P. Heinz, Jan 09 2017

Status

approved