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A123147 Multinomial based triangular function base on the sum of squares: out[n]=4*(n+2)!*(n*(n + 1)*(2*n + 1)/6)!/(4*(m^2)!*Abs[2 + 2*m^2 - (n*(n + 1)*(2*n + 1)/6)]!). 0
1, 6, 1, 480, 2880, 1, 21840, 2882880, 18162144000, 40040, 626400, 473558400, 3270820512960000, 145032891526185062400000, 380331009246988800000, 14968800, 41254012800, 22288874800832640000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

cubic generalization: T[n, m] = (a0*n^3+b0*n^2+c0*n+d0)!/(4*(m^2)!*Abs[2 + 2*m^2 - (a0*n^3+b0*n^2+c0*n+d0)]!)

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n,m) = (n*(n + 1)*(2*n + 1)/6)!/(4*(m^2)!*Abs[2 + 2*m^2 - (n*(n + 1)*(2*n + 1)/6)]!) out[n]=4*(n+2)!*a(n,m)

EXAMPLE

1

6, 1

480, 2880, 1

21840, 2882880, 18162144000, 40040

MATHEMATICA

T[n_, m_] = (n*(n + 1)*( 2*n + 1)/6)!/(4*(m^2)!*Abs[2 + 2*m^2 - (n*(n + 1)*(2*n + 1)/6)]!) a = Table[Table[4*(n + 2)!*T[n, m], {m, 0, n}], {n, 0, 10}] Flatten[a]

CROSSREFS

Sequence in context: A266302 A183284 A224476 * A119831 A224842 A318138

Adjacent sequences:  A123144 A123145 A123146 * A123148 A123149 A123150

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Oct 01 2006

STATUS

approved

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Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)