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A329754 Doubly pentagonal pyramidal numbers. 4
0, 1, 126, 3078, 32800, 213750, 1008126, 3783976, 11985408, 33297075, 83338750, 191592126, 410450976, 828497488, 1589341950, 2917620000, 5154021376, 8801526501, 14585352318, 23529456550, 37052820000, 57089119626, 86233820926, 127923156648, 186649920000, 268221484375, 380065968126 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

G.f.: x*(1 + 116*x + 1863*x^2 + 7570*x^3 + 9350*x^4 + 3474*x^5 + 304*x^6 + 2*x^7)/(1 - x)^10.

a(n) = A002411(A002411(n)).

a(n) = Sum_{k=0..A002411(n)} A000326(k).

a(n) = n^4 *(n^3+n^2+2) *(n+1)^2 /16. - R. J. Mathar, Nov 28 2019

MATHEMATICA

A002411[n_] := n^2 (n + 1)/2; a[n_] := A002411[A002411[n]]; Table[a[n], {n, 0, 26}]

Table[Sum[k (3 k - 1)/2, {k, 0, n^2 (n + 1)/2}], {n, 0, 26}]

nmax = 26; CoefficientList[Series[x (1 + 116 x + 1863 x^2 + 7570 x^3 + 9350 x^4 + 3474 x^5 + 304 x^6 + 2 x^7)/(1 - x)^10, {x, 0, nmax}], x]

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 126, 3078, 32800, 213750, 1008126, 3783976, 11985408, 33297075}, 27]

CROSSREFS

Cf. A000326, A002411, A140236, A232713, A329753, A329755, A329756, A329757.

Sequence in context: A113857 A267282 A008397 * A202593 A293104 A267750

Adjacent sequences:  A329751 A329752 A329753 * A329755 A329756 A329757

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Nov 20 2019

STATUS

approved

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Last modified August 15 13:59 EDT 2022. Contains 356145 sequences. (Running on oeis4.)