A060493 A diagonal of A036969.

0, 1, 21, 147, 627, 2002, 5278, 12138, 25194, 48279, 86779, 148005, 241605, 380016, 578956, 857956, 1240932, 1756797, 2440113, 3331783, 4479783, 5939934, 7776714, 10064110, 12886510, 16339635, 20531511, 25583481, 31631257, 38826012, 47335512, 57345288, 69059848

Offset: 0

Author

Larry Reeves (larryr(AT)acm.org), Mar 20 2001

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000330, A036969, A351105.

Programs

PARI

a(n)=n*(n + 1)*(n + 2)*(2*n + 1)*(2*n + 3)*(5*n - 1)/360

Formula

From Benoit Cloitre, Mar 20 2004: (Start)

a(n) = n*(n + 1)*(n + 2)*(2*n + 1)*(2*n + 3)*(5*n - 1)/360.

a(n) = Sum_{k=1..n} k^2 * Sum_{i=1..k} i^2.

a(n) = Sum_{k=1..n} k^2*A000330(k). (End)

G.f.: -x*(4*x^3+21*x^2+14*x+1) / (x-1)^7. - Colin Barker, Dec 19 2012

a(n) = 2/(2*n)! * Sum_{j = 1..n} (-1)^(n+j) * j^(2*n+4) * binomial(2*n, n-j). - Peter Bala, Mar 31 2025

Extensions

Missing a(0)=0 inserted by Alois P. Heinz, Feb 19 2022