A283322 Row sums of triangle in A283321.

1, 2, 4, 22, 149, 1186, 10807, 110762, 1260289, 15757714, 214703831, 3165856882, 50220944017, 852735163034, 15429720661279, 296365775922106, 6021825238479617, 129039801791351842, 2908148713706872999, 68758376703814729154, 1701649010958291917521, 43990236798804135274282

Offset

0,2

Links

Indranil Ghosh, Table of n, a(n) for n = 0..400

G. N. Bakare, S. O. Makanjuola, Some Results on Properties of Alternating Semigroups, Nigerian Journal of Mathematics and Applications Volume 24,(2015), 184-192.

Formula

Bakare et al. give a formula, see Theorem 3.2.

Example

Row 3 of triangle A283321: 1, 3, 3, 9. So a(3) = 1 + 3 + 3 + 9 = 22. - Indranil Ghosh, Mar 16 2017

Mathematica

T[n_, k_]:=If[k==n, (n !/2), If[k==n - 1, n^2*(n - 1)!/2, Binomial[n, k]^2 * k !]]; t[n_, k_]:=If[n<2, 1, T[n, k]]; For[n=0, n<=20, Print[Sum[t[n, k], {k, 0, n}], " "]; n++] (* Indranil Ghosh, Mar 16 2017 *)

Prog

(PARI) T(n, k) = if(k==n, (n!/2), if(k==n - 1, n^2*(n - 1)!/2,  binomial(n, k)^2 * k!));
t(n, k) = if(n<2, 1, T(n, k));
{for(n=0, 21, print1(sum(k=0, n, t(n, k)), ", "))} \\ Indranil Ghosh, Mar 16 2017
(Python)
import math
f=math.factorial
def C(n, r): return f(n)/f(r)/f(n - r)
def T(n, k):
....if k==n: return f(n)/2
....elif k==n-1: return n**2 * f(n - 1) / 2
....else: return C(n, k)**2 * f(k)
i=0
l=[]
for n in range(0, 401):
....for k in range(0, n+1):
........if n<2: l+=[1, ]
........else: l+=[T(n, k), ]
....print str(i)+" "+str(sum(l))
....l=[]
....i+=1 # Indranil Ghosh, Mar 16 2017

Crossrefs

Cf. A283321.

Sequence in context: A309741 A110130 A259116 * A019025 A264729 A339781

Adjacent sequences: A283319 A283320 A283321 * A283323 A283324 A283325

Keyword

nonn

Author

N. J. A. Sloane, Mar 15 2017

Status

approved