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A331987 a(n) = ((n + 1) - 9*(n + 1)^2 + 8*(n + 1)^3)/6. 2
0, 5, 23, 62, 130, 235, 385, 588, 852, 1185, 1595, 2090, 2678, 3367, 4165, 5080, 6120, 7293, 8607, 10070, 11690, 13475, 15433, 17572, 19900, 22425, 25155, 28098, 31262, 34655, 38285, 42160, 46288, 50677, 55335, 60270, 65490, 71003, 76817, 82940, 89380, 96145 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The start values of the partial rows on the main diagonal of A332662 in the representation in the example section.

Apparently the sum of the hook lengths over the partitions of 2*n + 1 with exactly 2 parts (cf. A180681).

LINKS

Table of n, a(n) for n=0..41.

FORMULA

a(n) = [x^n] (x*(3*x + 5))/(x - 1)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) = binomial(n+2, 3) + binomial(n+1, 3) + 2*(n+1)*binomial(n+1, 2).

MAPLE

a := n -> ((n+1) - 9*(n+1)^2 + 8*(n+1)^3)/6: seq(a(n), n=0..41);

gf := (x*(3*x + 5))/(x - 1)^4: ser := series(gf, x, 44):

seq(coeff(ser, x, n), n=0..41);

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {0, 5, 23, 62}, 42]

CROSSREFS

Apparently a bisection of A049779 and of A024862.

Cf. A180681, A332662.

Sequence in context: A159241 A179094 A176874 * A241765 A106956 A084671

Adjacent sequences:  A331984 A331985 A331986 * A331988 A331989 A331990

KEYWORD

nonn

AUTHOR

Peter Luschny, Feb 19 2020

STATUS

approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)