A207320 a(n) = Sum_{k=0..n-1} (-1)^k*k^2*A000172(k).

0, 0, -2, 38, -466, 5070, -51230, 495394, -4647646, 42658722, -385096770, 3431429230, -30256897090, 264500216510, -2295570216930, 19801160761630, -169902404575970, 1451166299240222, -12344920792691958, 104644181977065306, -884232602452034390, 7450498211688604010, -62617113713498946622, 525042133132770041538

Offset: 0

Author

N. J. A. Sloane, Feb 16 2012

Keywords

• sign

Links

• Z.-W. Sun, Congruences for Franel numbers, arXiv preprint arXiv:1112.1034, 2011.

Programs

Mathematica

a172[n_] := Sum[Binomial[2k, n] Binomial[2k, k] Binomial[2(n-k), n-k], {k, 0, n}]/2^n;
a[n_] := Sum[(-1)^k k^2 a172[k], {k, 0, n-1}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Feb 12 2019 *)