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A336020 a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} Stirling2(n-3,k) * a(k). 2
1, 1, 1, 1, 1, 2, 5, 15, 53, 222, 1115, 6698, 47243, 382187, 3480048, 35251942, 394839407, 4875966656, 66282636371, 989985346269, 16198580140543, 289168351452220, 5604120791540468, 117309414122840454, 2639927837211705159, 63618153549702851338 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Shifts left 3 places under Stirling transform.

LINKS

Table of n, a(n) for n=0..25.

FORMULA

E.g.f. A(x) satisfies A(x) = 1 + x + x^2/2 + Integral( Integral( Integral A(exp(x) - 1) dx) dx) dx.

MATHEMATICA

a[0] = a[1] = a[2] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 25}]

nmax = 25; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + Integrate[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!

PROG

(PARI) lista(nn) = {my(va = vector(nn, k, 1)); for (n=4, nn, va[n] = sum(k=0, n-3, stirling(n-4, k, 2)*va[k+1]); ); va; } \\ Michel Marcus, Jul 06 2020

CROSSREFS

Cf. A003659, A007469, A336021, A336022.

Sequence in context: A022493 A284729 A006966 * A277175 A056841 A185040

Adjacent sequences:  A336017 A336018 A336019 * A336021 A336022 A336023

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 05 2020

STATUS

approved

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Last modified May 12 01:50 EDT 2021. Contains 343808 sequences. (Running on oeis4.)