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A275872 A binomial convolution recurrence sequence. 1
0, 0, 1, 1, 2, 6, 18, 54, 173, 605, 2274, 9020, 37486, 163128, 743101, 3535765, 17518018, 90126158, 480514430, 2650912738, 15112253425, 88903779401, 539003066674, 3363608949132, 21581457167994, 142227480847092, 961868098767105, 6669657795455817, 47380035801732034, 344555811578909254, 2563218995058696890 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Shifts 2 places left and decreases by one under a variant of binomial transform (see formula section).

LINKS

Robert Israel, Table of n, a(n) for n = 0..648

FORMULA

Sum_{i=0..n} binomial(n+1,i+1)*a(i) = a(n+2) - 1.

G.f. g(x) satisfies g(x) = x^2/(1-x) + x^2*g(x/(1-x))/(1-x)^2. - Robert Israel, Aug 28 2016

MAPLE

A[0]:= 0:

A[1]:= 0:

for m from 2 to 50 do

  A[m]:= 1 + add(binomial(m-1, i+1)*A[i], i=0..m-2)

od:

seq(A[i], i=0..50); # Robert Israel, Aug 28 2016

MATHEMATICA

Clear[a]; a[0] = 0 ; a[1] = 0; a[n_] := a[n] = 1 + Sum[Binomial[n - 1, j+1]*a[j], {j, 0, n - 1}]; Table[a[n], {n, 0, 22}]

PROG

(PARI) first(n)=my(v=vector(n)); for(k=0, n-2, v[k+2]=sum(i=2, k, binomial(k+1, i+1)*v[i])+1); concat(0, v) \\ Charles R Greathouse IV, Aug 29 2016

CROSSREFS

Cf. A000994, A007476, A032346.

Sequence in context: A114464 A062415 A086680 * A148455 A094590 A004529

Adjacent sequences:  A275869 A275870 A275871 * A275873 A275874 A275875

KEYWORD

nonn,eigen,easy

AUTHOR

Olivier Gérard, Aug 11 2016

STATUS

approved

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Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)