A004344 Binomial coefficient C(5n+10,n).

1, 15, 190, 2300, 27405, 324632, 3838380, 45379620, 536878650, 6358402050, 75394027566, 895068996640, 10638894058520, 126600387152400, 1508152231077400, 17984495151670680, 214667221708410075, 2564603660132096265, 30664510802988208300, 366934961273420740200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A233738.

Programs

Magma

[Binomial(5*n+10,n) : n in [0..20]]; // Wesley Ivan Hurt, Sep 01 2014

Maple

A004344:=n->binomial(5*n+10,n): seq(A004344(n), n=0..20); # Wesley Ivan Hurt, Sep 01 2014

Mathematica

Table[Binomial[5 n + 10, n], {n, 0, 20}] (* Wesley Ivan Hurt, Sep 01 2014 *)

Formula

a(n) = C(5n+10,n) = (n+2)*A233738(n)/2. Wesley Ivan Hurt, Sep 01 2014

D-finite with recurrence 8*n*(2*n+5)*(4*n+7)*(4*n+9)*a(n) -5*(5*n+6)*(5*n+7)*(5*n+8)*(5*n+9)*a(n-1)=0. - R. J. Mathar, Mar 19 2025

Extensions

Name and offset changed by Wesley Ivan Hurt, Sep 01 2014