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A235595 Triangle read by rows: the triangle in A034855, with the n-th row normalized by dividing it by n. 5
1, 1, 2, 1, 9, 6, 1, 40, 60, 24, 1, 195, 560, 420, 120, 1, 1056, 5550, 6240, 3240, 720, 1, 6321, 59472, 94710, 68880, 27720, 5040, 1, 41392, 692440, 1527456, 1426320, 792960, 262080, 40320, 1, 293607, 8753040, 26418168, 30560544, 21213360, 9676800, 2721600, 362880, 1, 2237920, 119723130, 490458240 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Alois P. Heinz, Rows n = 2..142, flattened

FORMULA

A234953(n) = Sum_{k=1..n} k*T(n,k).

EXAMPLE

Triangle begins:

1.

1, 2,

1, 9, 6,

1, 40, 60, 24,

1, 195, 560, 420, 120,

1, 1056, 5550, 6240, 3240, 720,

1, 6321, 59472, 94710, 68880, 27720, 5040,

1, 41392, 692440, 1527456,1426320, 792960, 262080, 40320,

1, 293607, 8753040, 26418168, 30560544, 21213360, 9676800, 2721600, 362880,

...

MAPLE

b:= proc(n, h) option remember; `if`(min(n, h)=0, 1, add(

      binomial(n-1, j-1)*j*b(j-1, h-1)*b(n-j, h), j=1..n))

    end:

T:= (n, k)-> b(n-1, k-1)-b(n-1, k-2):

seq(seq(T(n, d), d=1..n-1), n=2..12);  # Alois P. Heinz, Aug 21 2017

MATHEMATICA

gf[k_] := gf[k] = If[k == 0, x, x*E^gf[k-1]]; a[n_, k_] := n!*Coefficient[Series[gf[k], {x, 0, n+1}], x, n]; t[n_, k_] := (a[n, k] - a[n, k-1])/n; Table[t[n, k], {n, 2, 11}, {k, 1, n-1}] // Flatten (* Jean-Fran├žois Alcover, Mar 18 2014, after Alois P. Heinz *)

PROG

(Python)

from sympy import binomial

from sympy.core.cache import cacheit

@cacheit

def b(n, h): return 1 if min(n, h)==0 else sum([binomial(n - 1, j - 1)*j*b(j - 1, h - 1)*b(n - j, h) for j in xrange(1, n + 1)])

def T(n, k): return b(n - 1, k - 1) - b(n - 1, k - 2)

for n in xrange(2, 13): print [T(n, d) for d in  xrange(1, n)] # Indranil Ghosh, Aug 26 2017, after Maple code

CROSSREFS

Cf. A000435, A034855, A001854, A210725, A234953, A235596, A236396.

Row sums give A000272.

Sequence in context: A155545 A141618 A061691 * A061356 A141028 A246323

Adjacent sequences:  A235592 A235593 A235594 * A235596 A235597 A235598

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jan 14 2014

STATUS

approved

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Last modified October 20 16:06 EDT 2018. Contains 316390 sequences. (Running on oeis4.)