The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A351811

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A351811

G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 5*x)) / (1 - 5*x)^2.
(history; published version)

#6 by Bruno Berselli at Sun Feb 20 06:46:17 EST 2022

STATUS

reviewed

approved

#5 by Joerg Arndt at Sun Feb 20 02:04:56 EST 2022

STATUS

proposed

reviewed

#4 by Ilya Gutkovskiy at Sat Feb 19 15:59:51 EST 2022

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Sat Feb 19 15:12:55 EST 2022

CROSSREFS

Cf. A005011, A040027, A351756, A351757, A351810, A351812.

#2 by Ilya Gutkovskiy at Sat Feb 19 15:07:55 EST 2022

NAME

allocated for Ilya Gutkovskiy

G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 5*x)) / (1 - 5*x)^2.

DATA

1, 1, 11, 101, 971, 10621, 133251, 1872261, 28840251, 481539021, 8658919571, 166768522101, 3421884596011, 74443313899901, 1710104876681571, 41338914172638021, 1048412294411955451, 27821558652073329261, 770663280948805164051, 22235353608667471453621

OFFSET

0,3

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 5^(k-1) * a(n-k).

MATHEMATICA

nmax = 19; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - 5 x)]/(1 - 5 x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

CROSSREFS

Cf. A005011, A040027, A351756, A351757.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Feb 19 2022

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sat Feb 19 15:07:55 EST 2022

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved