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A207622 Triangle of coefficients of polynomials u(n,x) jointly generated with A207623; see the Formula section. 3
1, 2, 4, 2, 7, 8, 11, 22, 4, 16, 50, 24, 22, 100, 88, 8, 29, 182, 252, 64, 37, 308, 616, 296, 16, 46, 492, 1344, 1032, 160, 56, 750, 2688, 3000, 896, 32, 67, 1100, 5016, 7656, 3696, 384, 79, 1562, 8844, 17688, 12496, 2528, 64, 92, 2158, 14872, 37752 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

With offset 0, equals the stretched Riordan array ((1 - z + z^2)/(1 - z)^3, 2*z^2/(1 - z)^2) in the notation of Corsani et al., Section 2. Cf. A207616. - Peter Bala, Dec 31 2015

LINKS

Table of n, a(n) for n=1..53.

C. Corsani, D. Merlini, R. Sprugnoli, Left-inversion of combinatorial sums Discrete Mathematics, 180 (1998) 107-122.

FORMULA

u(n,x) = u(n-1,x) + v(n-1,x), v(n,x) = 2*x*u(n-1,x) + v(n-1,x) + 1, where u(1,x) = 1, v(1,x) = 1.

EXAMPLE

First five rows:

   1

   2

   4  2

   7  8

  11 22  4

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + v[n - 1, x]

v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1

Table[Factor[u[n, x]], {n, 1, z}]

Table[Factor[v[n, x]], {n, 1, z}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A207622 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A207623 *)

CROSSREFS

Cf. A207623, A207616, A208510, A000124 (column 1).

Sequence in context: A207631 A207612 A207620 * A073017 A296092 A259111

Adjacent sequences:  A207619 A207620 A207621 * A207623 A207624 A207625

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)