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A283322 Row sums of triangle in A283321. 2
1, 2, 4, 22, 149, 1186, 10807, 110762, 1260289, 15757714, 214703831, 3165856882, 50220944017, 852735163034, 15429720661279, 296365775922106, 6021825238479617, 129039801791351842, 2908148713706872999, 68758376703814729154, 1701649010958291917521, 43990236798804135274282 (list; graph; refs; listen; history; text; internal format)
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 A192332

Adjacent sequences:  A283319 A283320 A283321 * A283323 A283324 A283325

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 15 2017

STATUS

approved

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Last modified April 5 13:02 EDT 2020. Contains 333241 sequences. (Running on oeis4.)