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A207318 a(n) = Sum_{k=0..n-1} (-1)^k*A000172(k). 0
0, 1, -1, 9, -47, 299, -1953, 13231, -91729, 647433, -4633499, 33531761, -244884159, 1802040241, -13346305519, 99392117841, -743734839215, 5588564785067, -42148760792553, 318928716891883, -2420342154102853, 18416484881248743, -140466988872011009, 1073705008744247231, -8223501739695527745 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..24.

Z.-W. Sun, Congruences for Franel numbers, arXiv preprint arXiv:1112.1034, 2011. See Eq. 1.5.

FORMULA

Conjecture: (n-1)^2*a(n) +(2*n-3)*(3*n-5)*a(n-1) +(-15*n^2+53*n-48)*a(n-2) +8*(n-2)^2*a(n-3)=0. - R. J. Mathar, Nov 28 2013

a(n) ~ (-1)^(n+1) * sqrt(3) * 2^(3*n+1) / (27*Pi*n). - Vaclav Kotesovec, Jan 31 2014

MATHEMATICA

Flatten[{0, Table[Sum[(-1)^k*Sum[Binomial[k, j]^3, {j, 0, k}], {k, 0, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jan 31 2014 *)

CROSSREFS

Sequence in context: A038740 A225428 A163614 * A293042 A159525 A173895

Adjacent sequences:  A207315 A207316 A207317 * A207319 A207320 A207321

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Feb 16 2012

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)