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

Author

Barry E. Williams, Dec 14 1999

Keywords

• easy
• nonn

Comments

Old name was: Partial sums of A051799.

References

• A. 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

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

Crossrefs

Cf. A051799.

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

A diagonal of A280880.

Programs

Mathematica

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

Formula

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

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

Extensions

Name changed by Alois P. Heinz, Jan 09 2017