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A211402 Triangle T(n,k), 0<=k<=n, given by (0,2,0,4,0,6,0,8,0,10,0,...) DELTA (1, 2, 3, 4, 5, 6, 7, 8, 9,...) where DELTA is the operator defined in A084938. 2
1, 0, 1, 0, 2, 3, 0, 4, 18, 15, 0, 8, 84, 180, 105, 0, 16, 360, 1500, 2100, 945, 0, 32, 1488, 10800, 27300, 28350, 10395, 0, 64, 6048, 72240, 294000, 529200, 436590, 135135, 0, 128, 24384, 463680, 2857680, 7938000, 11060280, 7567560, 2027025 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A Galton triangle. Essentially the same as A187075.

LINKS

Table of n, a(n) for n=0..44.

FORMULA

T(n,k) = 2*k*T(n-1,k) + (2*k-1)*T(n-1,k-1), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n.

T(n,k) = 2^(n-k)*A001147(k)*A048993(n,k).

G.f.: F(x,t) = 1 + x*t + (2*x+3*x^2)*t^2/2! + (4*x+18*x^2+15*x^3)*t^3/3!+ ... = Sum_{n = 0..inf}R(n,x)*t^n/n!.

The row polynomials R(n,x) satisfy the recursion R(n+1,x) = 2*(x+x^2)*R'(n,x) + x*R(n,x) where ' indicates differentiation with respect to x.

EXAMPLE

Triangle begins :

1

0, 1

0, 2, 3

0, 4, 18, 15

0, 8, 84, 180, 105

0, 16, 360, 1500, 2100, 945

0, 32, 1488, 10800, 27300, 28350, 10395

CROSSREFS

Cf. A000079, A001147, A048993.

Sequence in context: A261275 A140326 A261781 * A256064 A126436 A102394

Adjacent sequences:  A211399 A211400 A211401 * A211403 A211404 A211405

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 09 2013

STATUS

approved

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)